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Notes on Set Theory
Taschenbuch von Yiannis Moschovakis
Sprache: Englisch

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Beschreibung
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.
Zusammenfassung

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation. The book is geared to advanced undergraduate or beginning graduate mathematics students and mathematically minded graduate students in computer science and philosophy.

Inhaltsverzeichnis
Equinumerosity.- Paradoxes and Axioms.- Are Sets All There is?.- The Natural Numbers.- Fixed Points.- Well Ordered Sets.- Choices.- Choice's Consequences.- Baire Space.- Replacement and Other Axioms.- Ordinal Numbers.
Details
Erscheinungsjahr: 2005
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xii
278 S.
15 s/w Illustr.
274 farbige Illustr.
ISBN-13: 9780387287232
ISBN-10: 038728723X
Sprache: Englisch
Herstellernummer: 10993255
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Moschovakis, Yiannis
Auflage: 2nd ed. 2006
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 16 mm
Von/Mit: Yiannis Moschovakis
Erscheinungsdatum: 08.12.2005
Gewicht: 0,446 kg
Artikel-ID: 102270094
Zusammenfassung

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation. The book is geared to advanced undergraduate or beginning graduate mathematics students and mathematically minded graduate students in computer science and philosophy.

Inhaltsverzeichnis
Equinumerosity.- Paradoxes and Axioms.- Are Sets All There is?.- The Natural Numbers.- Fixed Points.- Well Ordered Sets.- Choices.- Choice's Consequences.- Baire Space.- Replacement and Other Axioms.- Ordinal Numbers.
Details
Erscheinungsjahr: 2005
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xii
278 S.
15 s/w Illustr.
274 farbige Illustr.
ISBN-13: 9780387287232
ISBN-10: 038728723X
Sprache: Englisch
Herstellernummer: 10993255
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Moschovakis, Yiannis
Auflage: 2nd ed. 2006
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 16 mm
Von/Mit: Yiannis Moschovakis
Erscheinungsdatum: 08.12.2005
Gewicht: 0,446 kg
Artikel-ID: 102270094
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