Pseudofinite Formulae

N. D. Markhabatov, Sergey Vladimirovich Sudoplatov

2022

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DOI 10.1134/s1995080222150215
Data confidence 70 medium
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Abstract

The concept of a pseudofinite formula is introduced. Links of pseudofinite formulae and their spectra are studied. Boolean algebras, lattices and semilattices related to pseudofinite formulae are found. Relations between pseudofinite formulae and positive, negative, $$\forall$$ -formulae, $$\exists$$ -formulae, $$\exists\forall$$ -formulae, $$\forall\exists$$ -formulae are considered. The family of all consistent formulae in a given language is considered and the existence of non-pseudofinite consistent formulae in that language is characterized.