Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-first-Century Semantics

History and Philosophy of Logic 23 (2):77-94 (2002)

Authors
Erich Reck
University of California, Riverside
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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DOI 10.1080/0144534021000028619
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References found in this work BETA

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
Logic in the Twenties: The Nature of the Quantifier.Warren D. Goldfarb - 1979 - Journal of Symbolic Logic 44 (3):351-368.

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Carnap's Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.

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