David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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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References found in this work BETA
H. Jerome Keisler (1965). Some Applications of Infinitely Long Formulas. Journal of Symbolic Logic 30 (3):339-349.
Karel Louis de Bouvère (1959). A Method in Proofs of Undefinability. Amsterdam, North-Holland Pub. Co..
Fred Galvin (1970). Horn Sentences. Annals of Mathematical Logic 1 (4):389-422.
Walter Taylor (1982). Equational Logic. Journal of Symbolic Logic 47 (2):450-450.
George Grätzer (1982). Universal Algebra. Studia Logica 41 (4):430-431.
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