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  1. (1 other version)Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
    Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.
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  • Completeness and categoricty, part II: 20th century metalogic to 21st century semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):77-92.
    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 (...)
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