Naslov
Existential definability of modal frame classes

Autori
Perkov, Tin ; Mikec, Luka

Izvornik
Mathematical logic quarterly (0942-5616) 66 (2020); 316-325

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
modal logic ; model theory ; modal definability

Sažetak
We prove an existential analogue of Goldblatt-Thomason theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of Goldblatt-Thomason theorem gives general conditions, without the assumption of first-order definability, but uses non-standard constructions and algebraic semantics. We present a non-algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable under any valuation (the so-called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first-order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well-known modal logics.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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