Sets and Extensions in the Twentieth Century

Edited by

  • Dov M. Gabbay, King's College London, UK
  • Akihiro Kanamori
  • John Woods, University of British Columbia, Vancouver, Canada

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration
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Audience

Researchers and graduate students in all areas of logic: Historians of logic, cognitive psychologists, computer scientists, mathematicians

 

Book information

  • Published: January 2012
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-51621-3


Table of Contents

Set Theory from Cantor to Cohen, by Akihiro Kanamori
History of the Continuum in the 20th Century, by Juris Steprans
Infinite Combinatorics, by Jean A. Larson
Large Cardinals with Forcing, by Akihiro Kanamori
Inner Models for Large Cardinals, by William J. Mitchell
A Brief History of Determinacy, by Paul B. Larson
Singular Cardinals: From Hausdorff’s Gaps to Shelah’s pcf Theory, by Menachem Kojman
Alternative Set Theories, by M. Randall Holmes, Thomas Forster, and Thierry Libert
Types, Sets, and Categories, by John L. Bell
The History of Categorical Logic: 1963-1977, by Jean-Pierre Marquis and Gonzalo E. Reyes
Russell’s Orders in Kripke’s Theory of Truth and Computational Type Theory, by Fairouz Kamareddine, Twan Laan, and Robert Constable