Completeness and Categoricity. Part I: Nineteenth-century Axiomatics to Twentieth-century Metalogic

History and Philosophy of Logic 23 (1):1-30 (2002)

Authors
Erich Reck
University of California, Riverside
Abstract
This paper is the first 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 10.1080/01445340210146889
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References found in this work BETA

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Introduction to Mathematical Logic.ALONZO CHURCH - 1956 - Princeton: Princeton University Press.
Introduction to Mathematical Logic.ALONZO CHURCH - 1944 - London: Oxford University PRess.
Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.

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Citations of this work BETA

Second Order Logic or Set Theory?Jouko Väänänen - 2012 - Bulletin of Symbolic Logic 18 (1):91-121.
Carnap's Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
Axioms in Mathematical Practice.D. Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.

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