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Zermelo's Axiom of Choice: Its Origins, Development, and Influence
- Gregory H. Moore
- Economics
- 17 November 1982
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 Implicit…
Collected Works, Volume I, Publications 1929-1936
- S. Feferman, J. Dawson, S. Kleene, Gregory H. Moore, R. Solovay
- Philosophy
- 1987
The emergence of first-order logic
- Gregory H. Moore
- Philosophy
- 1988
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 mathematician…
Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory
- Gregory H. Moore
- Philosophy
- 1980
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,…
Burali-Forti's paradox: A reappraisal of its origins
- Gregory H. Moore, A. Garciadiego
- Philosophy
- 1 August 1981
The axiomatization of linear algebra: 1875-1940
- Gregory H. Moore
- Mathematics
- 1995
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, nor…
Hilbert and the emergence of modern mathematical logic
- Gregory H. Moore
- Philosophy
- 1 March 1997
Hilbert's unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional…
The origins of Zermelo's axiomatization of set theory
- Gregory H. Moore
- PhilosophyJ. Philos. Log.
- 1978
TLDR
The Dual Cantor-Bernstein Theorem and the Partition Principle
- B. Banaschewski, Gregory H. Moore
- PhilosophyNotre Dame J. Formal Log.
- 1 June 1990
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