A note on definability in equational logic

History and Philosophy of Logic 15 (2):189-199 (1994)
After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications and extensions of this result.Topics considered here include equational definability in first order logic, an extended notion of definability in equational logic and the synonymy of equational theories.The final two sections briefly review some of the history of equational logic
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DOI 10.1080/01445349408837231
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References found in this work BETA
Some Applications of Infinitely Long Formulas.H. Jerome Keisler - 1965 - Journal of Symbolic Logic 30 (3):339-349.
Horn Sentences.Fred Galvin - 1970 - Annals of Mathematical Logic 1 (4):389-422.
A Method in Proofs of Undefinability.Karel Louis de Bouvère - 1959 - Amsterdam: North-Holland Pub. Co..
Equational Logic.Walter Taylor - 1982 - Journal of Symbolic Logic 47 (2):450-450.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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