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

History and Philosophy of Logic 23 (1):1-30 (2002)
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 - 1944 - London: Oxford University PRess.
Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.

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Citations of this work BETA
Carnap's Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
Maximality Principles in Set Theory.Luca Incurvati - forthcoming - Philosophia Mathematica:nkw011.
Concept Formation and Scientific Objectivity: Weyl's Turn Against Husserl.Iulian D. Toader - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science 3 (2):281-305.

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