David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Similar books and articles
James Walmsley (2002). Categoricity and Indefinite Extensibility. Proceedings of the Aristotelian Society 102 (3):217–235.
James H. Schmerl (1980). Decidability and ℵ0-Categoricity of Theories of Partially Ordered Sets. Journal of Symbolic Logic 45 (3):585 - 611.
Jürgen Saffe (1984). Categoricity and Ranks. Journal of Symbolic Logic 49 (4):1379-1392.
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
John Corcoran, William Frank & Michael Maloney (1974). String Theory. Journal of Symbolic Logic 39 (4):625-637.
Olivier Lessmann (2005). Upward Categoricity From a Successor Cardinal for Tame Abstract Classes with Amalgamation. Journal of Symbolic Logic 70 (2):639 - 660.
Olli Koistinen (2003). Spinoza's Proof of Necessitarianism. Philosophy and Phenomenological Research 67 (2):283–310.
Sy-David Friedman & Martin Koerwien (2010). On Absoluteness of Categoricity in Abstract Elementary Classes. Notre Dame Journal of Formal Logic 52 (4):395-402.
Fernando Ferreira (1999). A Note on Finiteness in the Predicative Foundations of Arithmetic. Journal of Philosophical Logic 28 (2):165-174.
Added to index2009-04-15
Total downloads80 ( #37,366 of 1,725,260 )
Recent downloads (6 months)23 ( #39,522 of 1,725,260 )
How can I increase my downloads?