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We describe classes of ℓ-algebras (which are based on lattices) such that their finitely presented projective algebras are closed under finite direct product, that is, for which unification is filtering. This implies that unification in such classes is either unitary or nullary. Following ideas of S. Ghilardi [12, 14] we attempt to describe filtering unification in a variety by means of properties of factor-congruences of algebras of the variety. The results subsume some previous results, but not those of [14], and open new areas for applications like residuated lattices. In particular we show that filtering unification depends on the monoid operation, that is, unification is filtering in varieties generated by residuated lattices without zero divisors. This implies that unification in strict fuzzy logics such as SMTL, MTL and many others is unitary or nullary. [ABSTRACT FROM AUTHOR]

Gödel logic (alias Dummett logic) is the extension of intuitionistic logic by the linearity axiom. Symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives. Symmetric Gödel logic is the extension of symmetric intuitionistic logic (L. Esakia, C. Rauszer). The proof-intuitionistic calculus, the language of which is an enrichment of the language of intuitionistic logic by modal operator was investigated by Kuznetsov and Muravitsky. Bimodal symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives and two modal operators. Bimodal symmetric Gödel logic is embedded into an extension of (bimodal) Gödel-Löb logic (provability logic), the language of which contains disjunction, conjunction, negation and two (conjugate) modal operators. The variety of bimodal symmetric Gödel algebras, that represent the algebraic counterparts of bimodal symmetric Gödel logic, is investigated. Description of free algebras and characterization of projective algebras in the variety of bimodal symmetric Gödel algebras is given. All finitely generated projective bimodal symmetric Gödel algebras are infinite, while finitely generated projective symmetric Gödel algebras are finite. [ABSTRACT FROM AUTHOR]

By a unital ℓ-group we mean a lattice-ordered abelian group with a distinguished order unit. This paper is concerned with the category of finitely presented unital ℓ-groups. Using the duality between and a category of rational polyhedra, we will provide (i) a construction of finite limits and co-limits in ; (ii) a Cantor-Bernstein-Schröder theorem for finitely presented unital ℓ-groups; (iii) a proof that the fibered product of finitely generated projective unital ℓ-groups is projective; (iv) a geometrical characterization of exact unital ℓ-groups. [ABSTRACT FROM AUTHOR]

In this paper, we study projective algebra, p(M, F), of special (α, β)-metrics. The projective algebra of a Finsler space is a finite-dimensional Lie algebra with respect to the usual Lie bracket. We characterize p(M, F) of Matsumoto and square metrics of isotropic S-curvature of dimension n ≥ 3 as a certain Lie sub-algebra of the Killing algebra k(M, α). We also show that F has a maximum projective symmetry if and only if F either is a Riemannian metric of constant sectional curvature or locally Minkowskian. [ABSTRACT FROM AUTHOR]

We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments. [ABSTRACT FROM AUTHOR]

The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2.