scholarly journals Non-finite axiomatizability of dynamic topological logic

2014 ◽  
Vol 15 (1) ◽  
pp. 1-18 ◽  
Author(s):  
David Fernández-Duque
Keyword(s):  
Finite Axiomatizability ◽  
Dynamic Topological Logic

The problem of finite axiomatizability for strongly minimal graph theories

1989 ◽  
Vol 28 (3) ◽  
pp. 183-194 ◽  
Author(s):  
A. A. Ivanov
Keyword(s):  
Finite Axiomatizability ◽  
Minimal Graph

scholarly journals On the Decidability of Intuitionistic Tense Logic without Disjunction

2020 ◽  
Author(s):  
Fei Liang ◽  
Zhe Lin
Keyword(s):  
Proof Theory ◽  
Tense Logic ◽  
Heyting Algebras ◽  
Finite Model ◽  
Algebraic Proof ◽  
Model Property ◽  
Algebraic Models ◽  
Finite Axiomatizability ◽  
Finite Model Property ◽  
Modal Operators

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

On the finite axiomatizability of ∀Σ̂1b(R̂21)

2018 ◽  
Vol 64 (1-2) ◽  
pp. 6-24
Author(s):  
Chris Pollett
Keyword(s):  
Finite Axiomatizability

scholarly journals Some results on finite axiomatizability in modal logic.

1965 ◽  
Vol 6 (4) ◽  
pp. 301-308 ◽  
Author(s):  
E. J. Lemmon
Keyword(s):  
Modal Logic ◽  
Finite Axiomatizability

On Dynamic Topological Logic of the Real Line

2008 ◽  
Vol 18 (6) ◽  
pp. 1029-1045 ◽  
Author(s):  
M. Nogin ◽  
A. Nogin
Keyword(s):  
Real Line ◽  
The Real ◽  
Dynamic Topological Logic

ON NON FINITE AXIOMATIZABILITY OF n-MODAL LOGICS BETWEEN AND FOR FINITE

2020 ◽  
Vol 47 (1) ◽  
pp. 99-119
Author(s):  
Tarek Sayed Ahmed
Keyword(s):  
Modal Logics ◽  
Finite Axiomatizability

Finite axiomatizability for equational theories of computable groupoids

1989 ◽  
Vol 54 (3) ◽  
pp. 1018-1022 ◽  
Author(s):  
Peter Perkins
Keyword(s):  
Binary Operation ◽  
Finite Algebra ◽  
Equational Theory ◽  
Natural Numbers ◽  
Finite Axiomatizability ◽  
Finite Algebras ◽  
Equational Theories ◽  
Primitive Recursive ◽  
Positive Integers ◽  
Recursive Set

A computable groupoid is an algebra ‹N, g› where N is the set of natural numbers and g is a recursive (total) binary operation on N. A set L of natural numbers is a computable list of computable groupoids iff L is recursive, ‹N, ϕe› is a computable groupoid for each e ∈ L, and e ∈ L whenever e codes a primitive recursive description of a binary operation on N.Theorem 1. Let L be any computable list of computable groupoids. The set {e ∈ L: the equational theory of ‹N, ϕe› is finitely axiomatizable} is not recursive.Theorem 2. Let S be any recursive set of positive integers. A computable groupoid GS can be constructed so that S is inifinite iff GS has a finitely axiomatizable equational theory.The problem of deciding which finite algebras have finitely axiomatizable equational theories has remained open since it was first posed by Tarski in the early 1960's. Indeed, it is still not known whether the set of such finite algebras is recursively (or corecursively) enumerable. McKenzie [7] has shown that this question of finite axiomatizability for any (finite) algebra of finite type can be reduced to that for a (finite) groupoid.

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