More on expressibility of satisfiability in submodels and extensions

Fuente: arXiv
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Main Authors: Poliakov, Nikolai L., Saveliev, Denis I.
Format: Preprint
Published: 2026
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author Poliakov, Nikolai L.
Saveliev, Denis I.
author_facet Poliakov, Nikolai L.
Saveliev, Denis I.
contents We study expressibility in infinitary languages of the modal operators associated with satisfiability of sentences of these languages in submodels and extensions of models. We give a syntactic criterion for expressibility in finitary predicate languages, show that in many cases infinitary languages are closed under the operator associated with submodels, and that this is so in any language with a purely monadic signature. Finally, we prove that in finitary or strongly compact languages, the operator associated with extensions, though can be inexpressible by a single sentence, is always expressible by a universal theory, in striking contrast with the submodel case.
format Preprint
id arxiv_https___arxiv_org_abs_2605_02725
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle More on expressibility of satisfiability in submodels and extensions
Poliakov, Nikolai L.
Saveliev, Denis I.
Logic
Primary 03B45, 03C75 Secondary 03C52, 03C85, 03E10, 03E55
We study expressibility in infinitary languages of the modal operators associated with satisfiability of sentences of these languages in submodels and extensions of models. We give a syntactic criterion for expressibility in finitary predicate languages, show that in many cases infinitary languages are closed under the operator associated with submodels, and that this is so in any language with a purely monadic signature. Finally, we prove that in finitary or strongly compact languages, the operator associated with extensions, though can be inexpressible by a single sentence, is always expressible by a universal theory, in striking contrast with the submodel case.
title More on expressibility of satisfiability in submodels and extensions
topic Logic
Primary 03B45, 03C75 Secondary 03C52, 03C85, 03E10, 03E55
url https://arxiv.org/abs/2605.02725