BETH DEFINABILITY IN INSTITUTIONS MARIUS PETRIA∗ AND RĂZVAN DIACONESCU Abstract. This paper studies definability within the theory of institutions, a version of abstract model This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definab...

Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, r...

We present results on global definability in basic modal logic, and contrast our model-theoretic results and proof techniques with known results about local definability.

We discuss the relationship between discontinuity and definability in the Turing degrees, with particular reference to degree invariant solutions to Post’s Problem. Proofs of new results concerning definability in lower cones are outlined.

This paper is devoted to exploring modal definability of firstorder sentences and first-order definability of modal formulas. It investigates the decidability and the complexity of these problems within the class of all partitions.

We investigate systems of transitive models ZFC which are elementarily embeddable into each other and the influence definability properties on such systems.