Beth Definability in Institutions
نویسنده
چکیده
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 definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on ametaBirkhoffaxiomatizability property of the institution and constitutes a source for many new actual definability results, including definability in (fragments of) classical model theory. The third one gives a set of sufficient conditions for ‘borrowing’ definability properties from another institution via an ‘adequate’ encoding between institutions. The power of our general definability results is illustrated with several applications to (many-sorted) classical model theory and partial algebra, leading for example to definability results for (quasi-)varieties of models or partial algebras. Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic.
منابع مشابه
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A few results generalizing well-known classical model theory ones have been obtained in the framework of institutions these last two decades (e.g. Craig interpolation, ultraproduct, elementary diagrams). In this paper, we propose a generalized institutionindependent version of the Beth definability theorem.
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