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Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics

Awodey, Steve and Reck, Erich H. (2002) Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics. [Preprint]

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      Abstract

      This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics so as to shed new light on the relevant strengths and limits of higher-order logic.


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      Item Type: Preprint
      Keywords: axiomatic method
      Subjects: Specific Sciences > Mathematics
      Depositing User: Steve Awodey
      Date Deposited: 23 Jan 2002
      Last Modified: 07 Oct 2010 11:10
      Item ID: 545
      URI: http://philsci-archive.pitt.edu/id/eprint/545

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