Abstract Beth definability in institutions

摘要: This paper studies definability within the theory of institutions, a version abstract model that emerged in computing science software specification and semantics. We generalise concept to arbitrary logics, formalised as we develop three general results. One generalises classical Beth theorem by relying on interpolation properties institution. Another relies meta Birkhoff axiomatizability property institution constitutes source for many new actual results, including (fragments of) theory. The third one gives set sufficient conditions 'borrowing' from another via an 'adequate' encoding between institutions. power our results is illustrated with several applications (many-sorted) partial algebra, leading example (quasi-)varieties models or algebras. Many other are expected multitude logical systems institutions logic.