Paper Info
Title
Abstract Beth definability in institutions
Abstract
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 a meta Birkhoff axiomatizability 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.
Year
DOI
Venue
2006
10.2178/jsl/1154698588
JOURNAL OF SYMBOLIC LOGIC
DocType
Volume
Issue
Journal
71
3
ISSN
Citations 
PageRank 
0022-4812
8
0.52
References 
Authors
16
2
Name
Order
Citations
PageRank
Razvan Diaconescu157140.93
Marius Petria2182.04