Set Theory with a Universal Set: Exploring an Untyped Universe

Hardcover | May 1, 1993

byT. E. Forster

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Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by othersets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed inthese non-standard set theories has been boosted by their relevance to computer science.The second edition still concentrates largely on Quine's New Foundations, reflecting the author's belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the settheories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.

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From Our Editors

This book is an essay: not a monograph, or a textbook, but an essay. It is intended to be a good read for those people who are already interested in this topic (or think they might be interested in it) rather than a comprehensive treatment for people who wish to master it, and a reference work for people who already have.

From the Publisher

Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by othersets, specifically to disallow the possibility o...

From the Jacket

This book is an essay: not a monograph, or a textbook, but an essay. It is intended to be a good read for those people who are already interested in this topic (or think they might be interested in it) rather than a comprehensive treatment for people who wish to master it, and a reference work for people who already have.

T. E. Forster is at University of Cambridge.

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Format:HardcoverDimensions:176 pages, 9.21 × 6.14 × 0.59 inPublished:May 1, 1993Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198514778

ISBN - 13:9780198514770

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Table of Contents

1. Introduction2. NF and related systems3. Permutation models4. Church-Oswald models5. Open problems6. Bibliography

From Our Editors

This book is an essay: not a monograph, or a textbook, but an essay. It is intended to be a good read for those people who are already interested in this topic (or think they might be interested in it) rather than a comprehensive treatment for people who wish to master it, and a reference work for people who already have.

Editorial Reviews

`...a lively introductin to the current research on NF''Maruice Boffa, Modern Logic