Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Poliakov, Nikolai L., Saveliev, Denis I.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160256529