Set Theory With a Universal Set: Exploring an Untyped Universe - Couverture rigide

Forster, T. E.

 
9780198514770: Set Theory With a Universal Set: Exploring an Untyped Universe
Couverture rigide
ISBN 10 : 0198514778 ISBN 13 : 9780198514770
Editeur : Clarendon Press, 1995

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Clarendon Press
Date d'édition
1995
Langue
anglais
ISBN 10 
0198514778
ISBN 13 
9780198514770
Reliure
Relié
Numéro d'édition
2
Nombre de pages
176
Coordonnées du fabricant
non disponible
Personne responsable
Ufficio Anagrafiche Messaggerie
ufficio.anagrafiche@meli.it

Via Verdi, 8
Assago Milano
20090
Italie

Autres éditions populaires du même titre

9780198533955: Set Theory With a Universal Set: Exploring an Untyped Universe

Edition présentée

ISBN 10 :  0198533950 ISBN 13 :  9780198533955
Editeur : Clarendon Press, 1992
Couverture rigide