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Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory
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Set Theory with a Universal Set - Exploring an Untyped Universe (Hardcover, 2nd Revised edition)
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Set Theory with a Universal Set - Exploring an Untyped Universe (Hardcover, 2nd Revised edition)
Series: Oxford Logic Guides, 31
Expected to ship within 12 - 17 working days
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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 other sets, 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
in these 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 set theories 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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