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THREE MODEL-THEORETIC CONSTRUCTIONS FOR GENERALIZED EPSTEIN SEMANTICS
- Part of
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- Journal:
- The Review of Symbolic Logic / Volume 15 / Issue 4 / December 2022
- Published online by Cambridge University Press:
- 08 July 2021, pp. 1023-1032
- Print publication:
- December 2022
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- Article
- Export citation
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This paper introduces three model-theoretic constructions for generalized Epstein semantics: reducts, ultramodels and
$\textsf {S}$-sets. We apply these notions to obtain metatheoretical results. We prove connective inexpressibility by means of a reduct, compactness by an ultramodel and definability theorem which states that a set of generalized Epstein models is definable iff it is closed under ultramodels and 
$\textsf {S}$-sets. Furthermore, a corollary concerning definability of a set of models by a single formula is given on the basis of the main theorem and the compactness theorem. We also provide an example of a natural set of generalized Epstein models which is undefinable. Its undefinability is proven by means of an 
$\textsf {S}$-set.
