Abstract
AbstractIn this paper, we consider predicate logic with two individual variables and general assignment models (where the set of assignments of the variables into a model is allowed to be an arbitrary subset of the usual one). We prove that there is a statement such that no general assignment model in which it is true can be finitely axiomatized. We do this by showing that the free relativized cylindric algebras of dimension two are not atomic.
Funder
Istanbul Medipol University
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. Andréka, H., J. D. Monk, and I. Németi, (eds.), Algebraic Logic, vol. 54 of Colloquia Mathematica Societatis János Bolyai, North Holland, Amsterdam, 1991.
2. Andréka, H., I. Hodkinson, and I. Németi, Finite algebras of relations are representable on finite sets, The Journal of Symbolic Logic 64(1):243–267, 1999.
3. Andréka, H., S. D. Comer, J. X. Madarász, I. Németi, and T. Sayed-Ahmed, Epimorphisms in cylindric algebras and definability in finite variable logic, Algebra Universalis 61:261–282, 2009.
4. Andréka, H., M. Ferenczi, and I. Németi, (eds.), Cylindric-like Algebras and Algebraic Logic, vol. 22 of Bolyai Society Mathematical Studies, Springer, 2013.
5. Banerjee, A., and M. Khaled, First order logic without equality on relativized semantics, Annals of Pure and Applied Logic 169(11):1227–1242, 2018.