Universal models and definability

Characterization, definability and separation via saturated models

Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies a modal logic L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of L-models can be defined by a formula or a set of formulas of L), and the Separation Theorem (that provides conditions under which two disjoint classes ...

Relative Definability and Models of Unary PCF

On Characterization, Definability and ω-Saturated Models

Two important classic results about modal expressivity are the Characterization and Definability theorems. We develop a general theory for modal logics below first order (in terms of expressivity) which exposes the following result: Characterization and Definability theorems hold for every (reasonable) modal logic whose ω-saturated models have the Hennessy-Milner property. The results are prese...

Characterizing Frame Definability in Team Semantics via the Universal Modality

Let ML( u) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the definability of ML( u) in the spirit of the well-known Goldblatt-Thomason-Theorem. We show that an elementary class F of Kripke frames is definable in ML( u) if and only if F is closed under taking generated subframes and bounded morphic ...

Resplendent Models and Σ1-definability with an Oracle

In this article we find some sufficient and some necessary Σ1-conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised backand-forth constructions and versions of the arithmeti...