David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 1 (1):187-207 (1980)
After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those involving the distinction between characterizing a system and axiomatizing the truths of a system
|Keywords||HISTORY PHILOSOPHY LOGIC MATHEMATICS CATEGORICITY CATEGORICAL SECOND-ORDER ISOMORPHISM COMPLETENESS CHURCH|
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References found in this work BETA
Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
Elliott Mendelson (1964). Introduction to Mathematical Logic. Princeton, N.J.,Van Nostrand.
Herbert B. Enderton (1972). A Mathematical Introduction to Logic. New York,Academic Press.
Citations of this work BETA
Georg Schiemer (2013). Carnap's Early Semantics. Erkenntnis 78 (3):487-522.
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic. History and Philosophy of Logic 23 (1):1-30.
Mirja Helena Hartimo (2007). Towards Completeness: Husserl on Theories of Manifolds 1890–1901. Synthese 156 (2):281 - 310.
Georg Schiemer (2012). Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity. Review of Symbolic Logic 5 (4):613-641.
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics. History and Philosophy of Logic 23 (2):77-94.
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