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650 results on '"Regular cardinal"'

3. On a geometric statement of Ramsey type.

Author

Kharazishvili, Alexander

Subjects
*RAMSEY numbers, *SET theory, *RAMSEY theory
Abstract

A simple geometric assertion of Ramsey type, concerning families of straight lines in the Euclidean space R 3 \mathbb{R}^{3} , is formulated, and it is shown that the assertion turns out to be undecidable within the framework of ZFC set theory. [ABSTRACT FROM AUTHOR]

Published
2022
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6. Problems

Author

Monk, J. Donald, Bass, Hyman, Series editor, Lu, Jiang-Hua, Series editor, Oesterlé, Joseph, Series editor, Tschinkel, Yuri, Series editor, and Monk, J. Donald

Published
2014
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7. Depth

Author

Monk, J. Donald, Bass, Hyman, Series editor, Lu, Jiang-Hua, Series editor, Oesterlé, Joseph, Series editor, Tschinkel, Yuri, Series editor, and Monk, J. Donald

Published
2014
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8. Cellularity

Author

Monk, J. Donald, Bass, Hyman, Series editor, Lu, Jiang-Hua, Series editor, Oesterlé, Joseph, Series editor, Tschinkel, Yuri, Series editor, and Monk, J. Donald

Published
2014
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9. Cardinals in Isabelle/HOL

Author

Blanchette, Jasmin Christian, Popescu, Andrei, Traytel, Dmitriy, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Kobsa, Alfred, editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Weikum, Gerhard, editor, Klein, Gerwin, editor, and Gamboa, Ruben, editor

Published
2014
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10. ψ1 AND THE MODAL μ-CALCULUS: In memory of Zoltán Ésik.

Author

GOUVEIA, MARIA JOÃO and SANTOCANALE, LUIGI

Subjects
CARDINAL numbers, CALCULUS, MEMORY, CONTINUOUS functions
Abstract

For a regular cardinal k, a formula of the modal μ-calculus is K-continuous in a variable x if, on every model, its interpretation as a unary function of x is monotone and preserves unions of K-directed sets. We define the fragment Cψ1 (x) of the modal μ-calculus and prove that all the formulas in this fragment are ttj.-continuous. For each formula ɸ(x) of the modal μ-calculus, we construct a formula ѱ(x) e Cψ1 (x) such that ɸ(x) is K-continuous, for some k, if and only if ɸ(x) is equivalent to ѱ(x). Consequently, we prove that (i) the problem whether a formula is K-continuous for some k is decidable, (ii) up to equivalence, there are only two fragments determined by continuity at some regular cardinal: the fragment Cψ0 (x) studied by Fontaine and the fragment Cψ1 (x). We apply our considerations to the problem of characterizing closure ordinals of formulas of the modal μ-calculus. An ordinal α is the closure ordinal of a formula ɸ(x) if its interpretation on every model converges to its least fixed-point in at most α steps and if there is a model where the convergence occurs exactly in α steps. We prove that ω1, the least uncountable ordinal, is such a closure ordinal. Moreover, we prove that closure ordinals are closed under ordinal sum. Thus, any formal expression built from 0,1, ω, ω1 by using the binary operator symbol + gives rise to a closure ordinal. [ABSTRACT FROM AUTHOR]

Published
2019
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11. Continuous images of closed sets in generalized Baire spaces

Author

Philipp Schlicht and Philipp Lücke

Subjects
Regular cardinal, Closed set, Statement (logic), continuous image, General Mathematics, Image (category theory), Mathematics::General Topology, Mathematics - Logic, regular cardinal, Combinatorics, Mathematics::Logic, closed subset, 03E05, 03E15, 03E35, 03E47, direct successor, FOS: Mathematics, Uncountable set, Arithmetic, Algebra over a field, dense open subset, Logic (math.LO), Kappa, Mathematics
Abstract

Let $\kappa$ be an uncountable cardinal with $\kappa=\kappa^{{\kappa^+$'' implies the statement "every closed subset of ${}^\kappa\kappa$ is a continuous image of ${}^\kappa(\kappa^+)$'' or its negation., Comment: 30 pages

Published
2023

24. Residual smallness in commutative algebra.

Author

Oman, Greg and Salminen, Adam

Subjects
COMMUTATIVE algebra, INFINITY (Mathematics), RING theory, IDENTITIES (Mathematics), MODULES (Algebra)
Abstract

In Oman and Salminen [19], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R∖{0}, there exists an ideal Ir of R such that r∉Ir and |R∕Ir|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. [ABSTRACT FROM AUTHOR]

Published
2018
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33. Trees

Author

Winkler, Peter, editor, Komjáth, Péter, and Totik, Vilmos

Published
2006
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36. Weak Bisimulation Approximants

Author

Harwood, Will, Moller, Faron, Setzer, Anton, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Ésik, Zoltán, editor

Published
2006
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37. Small $$\mathfrak {u}(\kappa )$$ at singular $$\kappa $$ with compactness at $$\kappa ^{++}$$

Author

Šárka Stejskalová and Radek Honzik

Subjects
Regular cardinal, Logic, 010102 general mathematics, Mathematics::General Topology, 0102 computer and information sciences, State (functional analysis), Lambda, Cofinality, 01 natural sciences, Combinatorics, Mathematics::Logic, Philosophy, Compact space, 010201 computation theory & mathematics, Uncountable set, Limit cardinal, 0101 mathematics, Kappa, Mathematics
Abstract

We show that the tree property, stationary reflection and the failure of approachability at $$\kappa ^{++}$$ are consistent with $$\mathfrak {u}(\kappa )= \kappa ^+ < 2^\kappa $$ , where $$\kappa $$ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if $$\lambda $$ is a regular cardinal, then stationary reflection at $$\lambda ^+$$ is indestructible under all $$\lambda $$ -cc forcings (out of general interest, we also state a related result for the preservation of club stationary reflection).

Published
2021

49. λ-Calculus as a Foundation for Mathematics

Author

Grue, Klaus, Hintikka, Jaakko, editor, Van Dalen, Dirk, editor, Davidson, Donald, editor, Kuipers, Theo A. F., editor, Suppes, Patrick, editor, Woleński, Jan, editor, Anderson, C. Anthony, editor, and Zelëny, Michael, editor

Published
2001
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