Автор |
Weaver, George |
Дата выпуска |
1994 |
dc.description |
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 |
Формат |
application.pdf |
Издатель |
Taylor & Francis |
Копирайт |
Copyright Taylor and Francis Group, LLC |
Название |
A note on definability in equational logic |
Тип |
research-article |
DOI |
10.1080/01445349408837231 |
Electronic ISSN |
1464-5149 |
Print ISSN |
0144-5340 |
Журнал |
History and Philosophy of Logic |
Том |
15 |
Первая страница |
189 |
Последняя страница |
199 |
Аффилиация |
Weaver, George; Department of Philosophy, Bryn Mawr College |
Выпуск |
2 |
Библиографическая ссылка |
Birkhoff, G. 1935. On the Structure of Abstract Algebras. Proceedings of the Cambridge Philosophical Society, 31: 433–454. |
Библиографическая ссылка |
De Bouvère, K. 1959. A Method In Proofs of Undecidability, Amsterdam: North Holland. |
Библиографическая ссылка |
De Bouvère, K. 1965. “Synonymous Theories”. In The Theory of Models, Edited by: Addison, J.W., Henkin, L. and Tarski, A. 402–406. Amsterdam: North Holland. |
Библиографическая ссылка |
Galvin, K. 1970. Horn Sentences. Annals of Mathematical Logic, 84: 389–422. |
Библиографическая ссылка |
Grätzer, G. 1968. Universal Algebra, Princeton: D.Van Nostrand. |
Библиографическая ссылка |
Hébert, M.R.N., Mckenzie, . and Weaver, G. 1989. Two Definability Results in the Equational Context. Proceedings of the American Mathematical Society, 107: 47–53. |
Библиографическая ссылка |
Henkin, L. 1977. The Logic of Equality. The American Mathematical Monthly, 84: 597–612. |
Библиографическая ссылка |
Kalicki, J. and Scott, D. 1955. Equational Completeness of Abstract Algebras. Indagationes Mathematicae, 17: 650–659. |
Библиографическая ссылка |
Keisler, H.J. 1965. Applications of Infinitely Long Formulas. Journal of Symbolic Logic, 30: 339–349. |
Библиографическая ссылка |
Monk, D. 1976. Mathematical Logic, New York: Springer Verlag. |
Библиографическая ссылка |
Padoa, A. 1967. “Logical Introduction to any deductive Theory”. In translated in From Frege to Gödel, Edited by: Heijenoort, Van. 118–123. Cambridge, Mass: Harvard University Press. |
Библиографическая ссылка |
Sheffer, H. 1913. A Set of Five Independent Postulates for Boolean Algebras, with Application to Logical Constants. Transactions AMS, 14: 481–488. |
Библиографическая ссылка |
Tarski, A. 1955. Contributions to the Theory of Models III. Indagationes Mathematicae, 17: 56–64. |
Библиографическая ссылка |
Tarski, A. 1968. “Equational Logic and Equational Theories of Algebra”. In Contributions to Mathematical Logic Edited by: Schmidt, H.A., Schütte, K. and Thiele, H.-J. 275–288. Amsterdam, North Holland |
Библиографическая ссылка |
Taylor, . 1979. Equational Logic, Houston Journal of Mathematics Survey. |