Notes on set theory
Whatthisbookisabout. Thetheoryofsetsisavibrant,excitingmathematical theory, with its own basic notions, fundamental results and deep open pr- lems,andwithsigni?cantapplicationstoothermathematicaltheories. Atthe sametime,axiomaticsettheoryisoftenviewedasafoundationofmathematics: it is allegedthat all...
Gardado en:
| Autor Principal: | |
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| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 2nd edition. |
| Series: | Undergraduate Texts in Mathematics
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Notes on set theory, Yiannis Moschovakis, 2nd edition, New York, Springer, 2006, 1 vol. (XII-276 p.), Undergraduate texts in mathematics, 0-387-28722-1 |
| Résumé: | Whatthisbookisabout. Thetheoryofsetsisavibrant,excitingmathematical theory, with its own basic notions, fundamental results and deep open pr- lems,andwithsigni?cantapplicationstoothermathematicaltheories. Atthe sametime,axiomaticsettheoryisoftenviewedasafoundationofmathematics: it is allegedthat all mathematical objectsare sets, and theirpropertiescan be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, making a notion precise is essentially s- onymouswith de?ningitinsettheory . Settheoryistheo?ciallanguageof mathematics,just asmathematicsisthe o?ciallanguageof science. Like most authors of elementary, introductory books about sets, I have triedtodojusticetobothaspectsofthesubject. From straight set theory, these Notes cover the basic facts about abstract sets , includingthe Axiom of Choice, trans?nite recursion, and cardinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on pointsets which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning. There is also some novelty in the approach to cardinal numbers, whichare brought in very early (following Cantor, but somewhatdeviously), so that the basic formulas of cardinal arithmetic can be taught as quickly as possible. AppendixAgivesamoredetailed construction oftherealnumbers thaniscommonnowadays,whichinadditionclaimssomenoveltyofapproach and detail. Appendix B is a somewhat eccentric, mathematical introduction to the study of natural models of various set theoretic principles, including Aczel s Antifoundation. It assumes no knowledge of logic, but should drive theseriousreaderto studyit. About set theory as a foundation of mathematics, there are two aspects of these Notes which are somewhat uncommon |
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| descrición da copia: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografía: | Index |
| ISBN: | 9780387316093 (En ligne) |
| ISSN: | 2197-5604 |
| Acceso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |