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The present paper is devoted to the Cauchy problem of inhomogeneous convolution equations of a fairly general nature. To solve the problems posed here, we apply the operator method proposed in some earlier papers by the author. The solutions of the problems under consideration are found using an effective method in the form of well-convergent vector-valued power series. The proposed method ensures the continuity of the obtained solutions with respect to the initial data and the inhomogeneous term of the equation. [ABSTRACT FROM AUTHOR]

The problem of ranking of elements from some finite set on the basis of nearest adjoining order method for pairwise comparisons is investigated in this paper. It is assumed that in the set under consideration there exists a weak preference relation, which is to be identified estimated) on the basis of pairwise comparisons in the form of difference of ranks. Moreover, the results of comparisons may be disturbed with random errors; the assumptions made about error distributions are not restrictive. The paper comprises: the problem formulation definitions, assumptions, and optimisation problem, which provides the NAO solution) and the theoretical background - the form of distributions of random variables which make it possible to determine the properties of NAO solution, in particular, evaluation of the probability, that the NAO solution is equivalent to the errorless one. The approach presented in the paper can be extended to the case of more than one comparison for each pair of elements, i.e., completely formalised multi-experts ranking procedure. [ABSTRACT FROM AUTHOR]

Research question: This paper examines the overarching question of to what extent different analytic choices may influence the inference about country-specific cross-sectional and trend estimates in international large-scale assessments. We take data from the assessment of PISA mathematics proficiency from the four rounds from 2003 to 2012 as a case study. Methods: In particular, four key methodological factors are considered as analytical choices in the rescaling and analysis of the data: (1) The selection of country sub-samples for item calibration differing at three factor levels. (2) The item sample refering to two sets of mathematics items used within PISA. (3) The estimation method used for item calibration: marginal maximum likelihood estimation method as implemented in R package TAM or an pairwise row averaging approach as implemented in the R package pairwise. (4) The type of linking method: concurrent calibration or separate calibration with successive chain linking. Findings: It turned out that analytical decisions for scaling did affect the PISA outcomes. The factors of choosing different calibration samples, estimation method and linking method tend to show only small effects on the country-specific cross-sectional and trend estimates. However, the selection of different link items seems to have a decisive influence on country ranking and development trends between and within countries. [ABSTRACT FROM AUTHOR]

The theorem proved in this paper establishes conditions under which a Banach space X is an Asplund space (i.e., its dual space is a space with the Radon-Nikodym (RN) property). The theorem is formulated in terms of the existence of a supersequentially compact set in ( B( X **), ω *), where B( X **) stands for the unit ball of the second dual of X and ω* for the weak topology on the ball. The example presented in the paper shows that one cannot get rid of some restrictive conditions in the theorem in general. [ABSTRACT FROM AUTHOR]

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. [ABSTRACT FROM AUTHOR]

Index sets are an integral and fundamental part of every mathematical modeling language. They assist the modeler in grouping various objects and entities. Index sets are also used extensively in the mathematical notation to write an expression in a concise way. An example is the sigma notation for formulating the summation of an unknown number n of terms. In this paper, the concept of index set is introduced in the context of modeling languages. The main objective is to propose an extension and generalization of the concept of index sets, which is the concept of hierarchical index sets. The paper concludes with an application, which clearly shows the usefulness of this concept. [ABSTRACT FROM AUTHOR]

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., 'Remarks on 'Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings',' Math. Comput. Modelling 54, 1467-1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

A generalized strong external difference family (briefly (v,m;k1,⋯,km;λ1,⋯,λm)-GSEDF) was introduced by Paterson and Stinson in 2016. In this paper, we give some nonexistence results for GSEDFs. In particular, we prove that a (v,3;k1,k2,k3;λ1,λ2,λ3)-GSEDF does not exist when k1+k2+k31, t>1 and v≡t≡1(mod2). Then we use it to obtain some new GSEDFs for m=2. In particular, for any prime power q with q≡1(mod4), we show that there exists a (qt,2;(q-1)2n-1,qt-12;(q-1)2n-2,(q-1)2n-2)-GSEDF, where t=p1p2⋯pn, pi>1, 1≤i≤n, p1,p2,⋯,pn are odd integers. [ABSTRACT FROM AUTHOR]

In this paper, the authors find the best numbers α and β such that for all a, b>0 with a≠ b, where $ \bar{C}(a,b)=\frac{2(a^{2}+ab+b^{2})}{3(a+b)}$ and $T(a,b)=\frac {2}{\pi }{\int }_{0}^{{\pi }/{2}}\sqrt {a^{2}{\cos ^{2}{\theta }}+b^{2}{\sin ^{2}{\theta }}}\, \mathrm {d} \theta $ denote respectively the centroidal mean and Toader mean of two positive numbers a and b. [ABSTRACT FROM AUTHOR]

In the model of Perfectly Secure Message Transmission Schemes (PSMTs), there are n channels between a sender and a receiver, and they share no key. An infinitely powerful adversary A can corrupt (observe and forge) the messages sent through some subset of n channels. For non-threshold adversaries called Q, Kumar et al. showed a many round PSMT (Ashwin Kumar et al. On perfectly secure communication over arbitrary networks. PODC 2002, pp. 193-202, ). In this paper, we show round efficient PSMTs against Q-adevrsaries. We first give a 3-round PSMT which runs in polynomial time in the size of the underlying linear secret sharing scheme. We next present a 2-round PSMT which is inefficient in general. (However, it is efficient for some special case.) [ABSTRACT FROM AUTHOR]

In this paper all cocyclic Hadamard matrices of order less than 40 are classified. That is, all such Hadamard matrices are explicitly constructed, up to Hadamard equivalence. This represents a significant extension and completion of work by de Launey and Ito. The theory of cocyclic development is discussed, and an algorithm for determining whether a given Hadamard matrix is cocyclic is described. Since all Hadamard matrices of order at most 28 have been classified, this algorithm suffices to classify cocyclic Hadamard matrices of order at most 28. Not even the total numbers of Hadamard matrices of orders 32 and 36 are known. Thus we use a different method to construct all cocyclic Hadamard matrices at these orders. A result of de Launey, Flannery and Horadam on the relationship between cocyclic Hadamard matrices and relative difference sets is used in the classification of cocyclic Hadamard matrices of orders 32 and 36. This is achieved through a complete enumeration and construction of (4 t, 2, 4 t, 2 t)-relative difference sets in the groups of orders 64 and 72. [ABSTRACT FROM AUTHOR]

Decision making is the process of finding the best option among the feasible alternatives. In classical multiple-criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy VIKOR method is presented, aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For application and verification, this study presents a numerical example and builds a practical maintenance strategy selection problem to verify our proposed method. Moreover, a comparison is made between the interval-valued fuzzy VIKOR and other adapted MCDM interval-valued fuzzy number-based. [ABSTRACT FROM AUTHOR]

The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint on mathematical practice. [ABSTRACT FROM AUTHOR]

In this paper I discuss possible ways of measuring the power of arithmetical theories, and the possiblity of making an explication in Carnap’s sense of this concept. Chaitin formulates several suggestions how to construct measures, and these suggestions are reviewed together with some new and old critical arguments. I also briefly review a measure I have designed together with some shortcomings of this measure. The conclusion of the paper is that it is not possible to formulate an explication of the concept. [ABSTRACT FROM AUTHOR]

Abstract  Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. [ABSTRACT FROM AUTHOR]

Abstract  In this paper we introduce new results in fuzzy connected spaces. Among the results obtained we can mention the good extension of local connectedness. Also we prove that in a T 1-fuzzy compact space the notions c-zero dimensional, strong c-zero dimensional and totally ci-disconnected are equivalent. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value −1 within LCZ. [ABSTRACT FROM AUTHOR]

The concepts of a tight set of points and an m-ovoid of a generalised quadrangle were unified recently by Bamberg, Law and Penttila under the title of intriguing sets. This unification was subsequently extended to polar spaces of arbitrary rank. The first part of this paper deals with a method of constructing intriguing sets of one polar space from those of another via field reduction. In the second part of this paper, we generalise an ovoid derivation of Payne and Thas to a derivation of intriguing sets. [ABSTRACT FROM AUTHOR]

The theorem proved in this paper gives a congruence for the traces of powers of an algebraic integer for the case in which the exponent of the power is a prime power. The theorem implies a congruence in Gauss’ form for the traces of the sums of powers of algebraic integers, generalizing many familiar versions of Fermat’s little theorem. Applied to the traces of integer matrices, this gives a proof of Arnold’s conjecture about the congruence of the traces of powers of such matrices for the case in which the exponent of the power is a prime power. [ABSTRACT FROM AUTHOR]

Suppose that K is a compact set in the open complex plane. In this paper, we prove an existence criterion for an estimate of Markov-Bernstein type for derivatives of a rational function R( z) at any fixed point z0 ∈ K. We prove that, for a fixed integer s, the estimate of the form | R( s) ( z0)| ≤ C( K, z0, s) n‖ R‖ C( K), where R is an arbitrary rational function of degree n without poles on K and C is a bounded function depending on three arguments K, z0, and s, holds if and only if the supremum over z in the complement of K is finite. Under this assumption, C is less than or equal to const · s!ω( K, z0, s). [ABSTRACT FROM AUTHOR]

The inherent dynamic relationships among design tasks performed concurrently at different organizations characterize the complexities of a design chain where designers with diverse expertise need to collaborate across organizational boundaries. To ensure timely completion of inter-related design tasks, metrics to facilitate the early evaluation of design concepts are crucial. The ability to evaluate and select suitable design concepts at an early stage will ensure better solutions and greater savings in time and effort further downstream. This paper proposes a new approach based on the rough set theory to design concept analysis. The approach aims at early detection of design inadequacy. A so-called information system is constructed using the information gleaned from design concepts and design capabilities, and analyzed using the rough set theory to derive a set of design rules for design concept analysis. The approach embodies a technique for handling attributes with unavailable information, which is a frequent occurrence in design. This paper presents details of the proposed approach, the novel technique, and a case study. [ABSTRACT FROM AUTHOR]

Let R be a ring and nil(R) the set of all nilpotent elements of R. For a subset X of a ring R, we define NR(X) = {a ϵ R ∣ xa ϵ nil(R) for all x ϵ X}; which is called the weak annihilator of X in R. In this paper we mainly investigate the properties of the weak annihilator over extension rings. [ABSTRACT FROM AUTHOR]

This paper investigates the relation between Carnap and Quine's views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine's own remarks, and set theory is at least defensibly analytic. [ABSTRACT FROM AUTHOR]

Ding and Feng (IEEE Trans Inform Theory 52(9):4229-4235, , IEEE Trans Inform Theory 53(11):4245-4250, ) constructed series of ( N, K) codebooks which meet or nearly meet the Welch bound $${\sqrt{\frac{N-K}{(N-1)K}}}$$ by using difference set (DS) or almost difference set (ADS) in certain finite abelian group respectively. In this paper, we generalize the cyclotomic constructions considered in (IEEE Trans Inform Theory 52(9):4229-4235, , IEEE Trans Inform Theory 53(11):4245-4250, ) and (IEEE Trans Inform Theory 52(5), 2052-2061, ) to present more series of codebooks which nearly meet the Welch bound under looser conditions than ones required by DS and ADS. [ABSTRACT FROM AUTHOR]

This article puts forward the notion of 'evolving diagram' as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter 'diagrams*') in the context of 'sketch theory,' a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively. [ABSTRACT FROM AUTHOR]

As a generalization of a BCK-algebra, a BE-algebras was introduced. In this paper, we investigate several properties of upper sets in BE-algebras, and we introduce more extended upper sets of BE-algebras, and obtain some relations with filters of BE-algebras. Also, the notion of Krull dimension of a BE-algebra and the notion of regular sequence in a BE-algebra are introduced. [ABSTRACT FROM AUTHOR]

This paper presents a method to find new de Bruijn sequences based on ones of lesser order. This is done by mapping a de Bruijn cycle to several vertex disjoint cycles in a de Bruijn digraph of higher order and then connecting these cycles into one full cycle. We present precise formulae for the locations where those cycles can be rejoined into one full cycle. We obtain an exponentially large class of distinct de Bruijn cycles. This method generalizes the Lempel construction of binary de Bruijn sequences as well as its efficient implementation by Annextein. [ABSTRACT FROM AUTHOR]

It is proved in the paper that the multiplication operation on an arbitrary E-algebra can be extended to an E-algebra A-morphism. As a corollary, it is proved that every May algebra defined by an E-algebra is a Cartan object in the category of May algebras. [ABSTRACT FROM AUTHOR]

It is well known that the MacWilliams transform of the weight enumerator of some code having integer coefficients is equivalent to a set of congruences having integer solutions. In this paper, we prove an equivalent condition of Ward's bound on dimension of divisible codes, which is part of this set of congruences having integer solutions. This new interpretation makes the generalization of Ward's bound an explicit one. [ABSTRACT FROM AUTHOR]

Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these criticisms are misguided by arguing that category theory is entirely autonomous from set theory. [ABSTRACT FROM AUTHOR]

In this paper, we derive some existence results for generalized variational inequalities associated with mappings satisfying the ( S)+ condition. The relation between the ( S)+ and ( S) conditions is discussed. As an application, we also consider multivalued complementarity problems associated with mappings satisfying the ( S)+ condition, and prove a theorem to characterize the solvability of such problems in terms of exceptional families of elements. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence of zero points for set-valued pseudomonotone operators in a Banach space by using a new condition which was recently proposed by the authors (Matsushita and Takahashi, Set-Valued Analysis 15:251–264, 2007). [ABSTRACT FROM AUTHOR]

Abstract  The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis. [ABSTRACT FROM AUTHOR]

Abstract  The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small. [ABSTRACT FROM AUTHOR]

Abstract  In De Bruyn Discrete math(to appear), one of the authors proved that there are six isomorphism classes of hyperplanes in the dual polar space DW(5, q), q even, which arise from its Grassmann-embedding. In the present paper, we determine the combinatorial properties of these hyperplanes. Specifically, for each such hyperplane H we calculate the number of quads Q for which $${Q \cap H}$$ is a certain configuration of points in Q and the number of points $${x \in H}$$ for which $${x^\perp \cap H}$$ is a certain configuration of points in $${x^\perp}$$ . By purely combinatorial techniques, we are also able to show that the set of hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding can be divided into six subclasses if one takes only into account the above-mentioned combinatorial properties. A complete classification of all hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding, i.e. the division of the above-mentioned six classes into isomorphism classes, will unlike in De Bruyn (to appear) most likely need a group-theoretical approach. [ABSTRACT FROM AUTHOR]

The article examines a perturbed Ostrowski-type inequality on time scales for k points for functions whose second derivatives are bounded. Authors of this paper have also point out some particular perturbed integral inequalities on time scales for functions whose second derivatives are bounded as special cases. These include perturbed rectangle inequality on time scales, perturbed trapezoid inequality on time scales, and perturbed mid-point inequality on time scales. The theory of time scales is considered as a theory capable to contain both difference and differential calculus in a consistent way.

Abstract  In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whether a given set of Boolean functions is a model for a formula. For classes of Boolean functions, we establish some characterizations in terms of classes of quantified Boolean formulas that have such a model. [ABSTRACT FROM AUTHOR]

This paper describes a parallel implementation of the Gröbner Bases algorithm and the Characteristic Sets method using a grid environment. The two algorithms, their parallelization, and grid-enabled implementations are presented. The performance of the implementations has been evaluated and the experiments have demonstrated considerable speedups. [ABSTRACT FROM AUTHOR]

As a first step of a project on learning difficulties in elementary set theory, we carried out a study aimed at identifying some of the difficulties encountered by a group of 21 mathematics majors taking a course on logic and set theory. In this paper, we shall discuss one of the difficulties that we observed, namely a difficulty in conceiving a set as an object distinct from its elements, i.e. failing to fully grant sets the status of objects. This difficulty may be related to the following three types of errors that we observed in the students' first assignment: (1) confusing belonging and inclusion, (2) confusing the union of sets A, B, C, ... with the set whose elements are A, B, C, ... and (3) adding or deleting curly brackets. We shall present excerpts from the students' work illustrating these three types of errors and explain how they may be related to a difficulty in conceiving a set as an object distinct from its elements. [ABSTRACT FROM AUTHOR]

Multisets are collections of objects which may include several copies of the same object. They may represent bundles of goods, committees formed of members of several political parties, or income streams. In this paper we investigate the ways in which a linear order on a finite set A can be consistently extended to an order on the set of all multisets on A of some given cardinality k and when such an extension arises from a utility function on A. The condition of consistency that we introduce is a close relative of the de Finetti's condition that defines comparative probability orders. We prove that, when A has three elements, any consistent linear order on multisets on A of cardinality k arises from a utility function and all such orders can be characterised by means of Farey fractions. This is not true when A has cardinality four or greater. It is proved that, unlike linear orders that can be represented by a utility function, any non-representable order on the set of all multisets of cardinality k cannot be extended to a consistent linear order on multisets of cardinality K for sufficiently large K. We also discuss the concept of risk aversion arising in this context. [ABSTRACT FROM AUTHOR]

In this paper, we solve the problem of reconstructing an arbitrary solution of a homogeneous convolution equation from its values at integer points of the real axis. [ABSTRACT FROM AUTHOR]

In this paper, the model approach to nonstandard analysis is developed on the basis of Zermelo—Fraenkel axiomatic set theory with atoms. The traditional consideration of the standard superstructure V as the primary object of nonstandard analysis is justified. Set-theoretic axioms for the nonstandard system * V are obtained. [ABSTRACT FROM AUTHOR]

We consider finite groups only. Let ω be a nonempty subset of the set P of all primes, and let f : ω ∪ {ω′} → {formations of groups} and δ : P → {nonempty Fitting formations of groups} be some functions. The formation consisting of all groups G such that $${G \mathord{\left/ {\vphantom {G O}} \right. \kern-\nulldelimiterspace} O}_\omega (G) \in f(\omega ')$$ and $${G \mathord{\left/ {\vphantom {G G}} \right. \kern-\nulldelimiterspace} G}_{\delta (p)} \in f(p)$$ for any p ∈ ω ∩ π ( G) is referred to as an ω-fan formation with direction δ. Let ℌ be some class of groups; an ω-fan formation $$\mathfrak{F}$$ with direction δ is said to be an ℌωδ-critical formation if $$\mathfrak{F}\not \subseteq \mathfrak{H}$$ and any proper ω-fan subformation with direction δ in $$\mathfrak{F}$$ is contained in the class ℌ. In the paper, a description of the structure of the ℌωδ-critical formations is presented. [ABSTRACT FROM AUTHOR]

In the paper, the set of exponents of exponential growth (growth exponents) for a finitely generated group with respect to all possible generators of this group is studied. It is proved that the greatest lower bound of this set is attained for the free products of a cyclic group of prime order and a free group of finite rank. [ABSTRACT FROM AUTHOR]

Abstract Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to ?0 formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals. [ABSTRACT FROM AUTHOR]

Abstract MLSS is a decidable fragment of set theory involving the predicates membership and set equality and the operators union, intersection, set difference, and singleton. In this paper we extend MLSS with the iterated membership predicate, that is, with a predicate denoting the transitive closure of the membership relation. We call the resulting language MLSS+. We prove that MLSS+ is decidable by providing a decision procedure for it based on Smullyan semantic tableaux. As an application of our results, we show how our decision procedure can be used as a black box in order to allow an interactive theorem prover to verify some basic properties of the ordinal numbers. [ABSTRACT FROM AUTHOR]

In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying (O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s). [ABSTRACT FROM AUTHOR]

In the first section of this paper I present the measurement-theoretic fallacy of 'over-assignment of structure': the unwarranted assumption that every numeric relation holding among two (or more) numbers represents some empirical, physical relation among the objects to which these numbers are assigned as measures (e.g., of temperature). In the second section I argue that a generalized form of this fallacy arises in various philosophical contexts, in the form of a misguided, over-extended application of one conceptual domain to another. Three examples are given: (i) the reduction of arithmetic into set theory, (ii) the ascription of full-blown intentional states to (at least some) non-overtly intentional creatures, such as Wittgenstein's builders, and (iii) the analysis of some modal notions as involving quantification over possible worlds (or their substitutes). The discussion of the third example gives rise to a novel account of possible-worlds talk. [ABSTRACT FROM AUTHOR]

Earlier, Belegradek, Stolboushkin, and Taitslin proved that the collapse result holds in the theory of natural numbers with addition, i.e., each locally generic query using addition can be written without it. In this paper, we use the sufficient conditions of the collapse result obtained by Taitslin to prove that it holds in any extensions of the Presburger arithmetic by a unary function compatible with addition. The notion of a function compatible with addition was proposed by A. L. Semenov. [ABSTRACT FROM AUTHOR]

In this paper we establish some conditions for an almost π-domain to be a π-domain. Next π-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for π-rings. [ABSTRACT FROM AUTHOR]