{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:14:06Z","timestamp":1760170446049,"version":"3.33.0"},"reference-count":52,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2749,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 \u2018borrowing\u2019 definability properties from another institution via an \u2018adequate\u2019 encoding between institutions.<\/jats:p><jats:p>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.<\/jats:p>","DOI":"10.2178\/jsl\/1154698588","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:23:20Z","timestamp":1198081400000},"page":"1002-1028","source":"Crossref","is-referenced-by-count":23,"title":["Abstract Beth definability in institutions"],"prefix":"10.1017","volume":"71","author":[{"given":"Marius","family":"Petria","sequence":"first","affiliation":[]},{"given":"R\u0103zvan","family":"Diaconescu","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006034_ref052","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(96)00146-9"},{"key":"S0022481200006034_ref048","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(85)90094-5"},{"key":"S0022481200006034_ref042","unstructured":"Popescu Andrei , \u015eerb\u0103nu\u0163\u0103 Traian , and Ro\u015fu Grigore , A semantic approach to interpolation, submitted."},{"first-page":"113","volume-title":"Logica universalis","author":"Mossakowski","key":"S0022481200006034_ref040"},{"key":"S0022481200006034_ref039","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00369-3"},{"key":"S0022481200006034_ref037","first-page":"18","volume-title":"Proceedings of the WADT'97","author":"Meseguer","year":"1998"},{"key":"S0022481200006034_ref036","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)90182-F"},{"key":"S0022481200006034_ref034","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1978-024-5"},{"key":"S0022481200006034_ref032","unstructured":"Lamo Yngve , The institution of multialgebras\u2014a general framework for algebraic software development, PhD thesis , University of Bergen, 2003."},{"key":"S0022481200006034_ref031","volume-title":"Introduction to higher order categorical 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