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Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
...a lively introductin to the current research onNF' (Maruice Boffa, Modern Logic)
Contenuti
- 1: Introduction
- 2: NF and related systems
- 3: Permutation models
- 4: Church-Oswald models
- 5: Open problems
- 6: Bibliography
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreClarendon Press
- Data di pubblicazione1995
- ISBN 10 0198514778
- ISBN 13 9780198514770
- RilegaturaCopertina rigida
- LinguaInglese
- Numero edizione2
- Numero di pagine176
- Contatto del produttorenon disponibile
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Set Theory with a Universal Set: Exploring an Untyped Universe: 31 (Oxford Logic Guides)
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Set Theory with a Universal Set: Exploring an Untyped Universe (Oxford Logic Guides, 31)
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Set Theory with a Universal Set (Hardcover)
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ISBN 10: 0198514778
ISBN 13: 9780198514770
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Hardcover. Condizione: new. Hardcover. 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 - theuniversal 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 computerscience.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 auseful and readable introduction for those interested in this topic, and a reference work for those already involved in this area. An expanded and revised edition of the introductory text, which can be used as a reference resource for those already working in the field. Forster focuses on Quine's original work, and has written a revised account of the set theories of Church-Oswald and Mitchell, with permutation models and extensions that preserve power sets. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780198514770
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Set Theory with a Universal Set (Hardcover)
Editore:
Oxford University Press, Oxford, 1995
ISBN 10: 0198514778
ISBN 13: 9780198514770
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Hardcover. Condizione: new. Hardcover. 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 - theuniversal 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 computerscience.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 auseful and readable introduction for those interested in this topic, and a reference work for those already involved in this area. An expanded and revised edition of the introductory text, which can be used as a reference resource for those already working in the field. Forster focuses on Quine's original work, and has written a revised account of the set theories of Church-Oswald and Mitchell, with permutation models and extensions that preserve power sets. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Codice articolo 9780198514770
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Set Theory with a Universal Set
Editore:
Oxford University Press OUP, 1995
ISBN 10: 0198514778
ISBN 13: 9780198514770
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Condizione: New. pp. 180. Codice articolo 262282493
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