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Zermelo's Axiom of Choice: Its Origins, Development, and Influence

- Gregory H. Moore
- Mathematics
- 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… Expand

251 5

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… Expand

58 2- PDF

Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory

- Gregory H. Moore
- Mathematics
- 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,… Expand

69 2

Burali-Forti's paradox: A reappraisal of its origins

- Gregory H. Moore, A. Garciadiego
- Mathematics
- 1 August 1981

Abstract Using both published and unpublished letters and manuscripts, this article shows that Burali-Forti's paradox, which has long been regarded as the first of the set-theoretical paradoxes to be… Expand

53 1

The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number

- Gregory H. Moore
- Philosophy
- 1995

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 letters… Expand

14 1

Hilbert on the Infinite: The Role of Set Theory in the Evolution of Hilbert's Thought

- Gregory H. Moore
- Mathematics
- 1 February 2002

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's… Expand

8 1

The Dual Cantor-Bernstein Theorem and the Partition Principle

- B. Banaschewski, Gregory H. Moore
- Mathematics, Computer Science
- Notre Dame J. Formal Log.
- 1 June 1990

TLDR

12 1

Early history of the Generalized Continuum Hypothesis: 1878 - 1938

- Gregory H. Moore
- Mathematics, Computer Science
- Bull. Symb. Log.
- 1 December 2011

TLDR

10 1- PDF

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… Expand

30 1- PDF

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