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Zermelo’s Axiom of Choice
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Zermelo's Axiom of Choice: Its Origins, Development, and Influence
Prologue.- 1 The Prehistory of the Axiom of Choice.- 1.1 Introduction.- 1.2 The Origins of the Assumption.- 1.3 The Boundary between the Finite and the Infinite.- 1.4 Cantor's Legacy of ImplicitExpand
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The emergence of first-order logic
To most mathematical logicians working in the 1980s, first-order logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematicianExpand
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Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory
What has been the historical relationship between set theory and logic? On the one hand, Zermelo and other mathematicians developed set theory as a Hilbert-style axiomatic system. On the other hand,Expand
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Burali-Forti's paradox: A reappraisal of its origins
Abstract Using both published and unpublished letters and manuscripts, this article shows that Burali-Forti's paradox, which has long been regarded as the first of the set-theoretical paradoxes to beExpand
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The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number
From 1897 to 1913, during the entire period when Russell made his major contributions to mathematical logic, he corresponded regularly with the French philosopher, Louis Couturat. Almost 200 lettersExpand
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Hilbert on the Infinite: The Role of Set Theory in the Evolution of Hilbert's Thought
Abstract Although Hilbert created no new set-theoretic theorems, he had a profound effect on the development of set theory by his advocacy of its importance. This article explores Hilbert'sExpand
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The Dual Cantor-Bernstein Theorem and the Partition Principle
TLDR
This paper examines two propositions, the Dual Cantor-Bernstein Theorem and the Partition Principle, with respect to their logical interrelationship and their history. Expand
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Early history of the Generalized Continuum Hypothesis: 1878 - 1938
TLDR
GCH arose from Cantor's Continuum Hypothesis in the work of Peirce, Jourdain, Hausdorff, Tarski, and how GCH was used up to Godel's relative consistency result. Expand
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The axiomatization of linear algebra: 1875-1940
Modern linear algebra is based on vector spaces, or more generally, on modules. The abstract notion of vector space was first isolated by Peano (1888) in geometry. It was not influential then, norExpand
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