WebNov 4, 2007 · It is known that Q(τ ) is a finitely axiomatizable quasivariety if τ ⊆ {0, 1, +, · , −, 1 , }. ... Positive fragments of relevance logic and algebras of binary relations Article WebApr 3, 2024 · In logic with identity, T has a finitely axiomatizable conservative extension that does not add new variable types iff T is Σ 1 1 in second order logic. The set of infinite models of T is always Σ 1 1. For finite structures, being a model of T is Σ 1 1 iff it is NP. Now, for finite structures, being a model P A t o p is axiomatizable by a ...
axiomatizable class - PlanetMath
WebFor obvious reasons, elementary classes are also called axiomatizable in first-order logic, and basic elementary classes are called finitely axiomatizable in first-order logic. These definitions extend to other logics in the obvious way, but since the first-order case is by far the most important, axiomatizable implicitly refers to this case ... A class K of structures of a signature σ is called an elementary class if there is a first-order theory T of signature σ, such that K consists of all models of T, i.e., of all σ-structures that satisfy T. If T can be chosen as a theory consisting of a single first-order sentence, then K is called a basic elementary class. More generally, K is a pseudo-elementary class if there is a first-order theory T of a signature tha… to follow the company rule
Pseudofinite Formulae SpringerLink
WebJun 12, 2024 · RA is finitely axiomatizable, hence provability of a sentence Q over RA is equivalent to provability of a single sentence over pure FOL (i.e. the conjunction of RA's axioms implies Q). Since provability of RA is undecidable by Godel-Rosser, provability over pure FOL is also undecidable. WebDec 24, 2024 · It'll be finitely axiomatizable since also NBG would be an extension of it by finitely many axioms. $\endgroup$ – Zuhair Al-Johar. Dec 25, 2024 at 10:13 $\begingroup$ Finite axiomatizability is preserved upwards by adding finitely many axioms, but not preserved downwards. So the finite axiomatizability of NBG does not imply finite ... Web2 Answers. Suppose ZF is consistent and ZF is fnitely axiomatizable. Let Γ ⊂ ZF be a finite subset such that Γ ⊢ ZFC. Referring to Jech or Kunen, ZF ⊢ Reflection Theorem. So ZF … to follow the company\u0027s rule