The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics) - gebunden oder broschiert

EAN (ISBN-13): 9780387940946
ISBN (ISBN-10): 0387940944
Gebundene Ausgabe
Erscheinungsjahr: 2007
Herausgeber: Springer
212 Seiten
Gewicht: 0,485 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-06-13T11:34:14+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-04-04T22:16:08+02:00 (Berlin)
ISBN/EAN: 0387940944

ISBN - alternative Schreibweisen:
0-387-94094-4, 978-0-387-94094-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: devlin keith, fraenkel
Titel des Buches: theory sets, set theory, fundamental mathematics, the fundamentals, devlin, joy less, contemporary mathematics, inner joy, none the above contemporary, undergraduate text

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Daten vom Verlag:

Autor/in: Keith Devlin
Titel: Undergraduate Texts in Mathematics; The Joy of Sets - Fundamentals of Contemporary Set Theory
Verlag: Springer; Springer US
194 Seiten
Erscheinungsjahr: 1993-08-03
New York; NY; US
Sprache: Englisch
59,87 € (DE)
61,55 € (AT)
86,67 CHF (CH)
Available
X, 194 p.

BB; Hardcover, Softcover / Mathematik/Grundlagen; Mathematik: Logik; Verstehen; Cardinal number; computer science; mathematics; proof; set theory; sets; Mathematical Logic and Foundations; Mathematical Applications in Computer Science; Mathematische Grundlagen; Theoretische Informatik; BC

1 Naive Set Theory.- 1.1 What is a Set?.- 1.2 Operations on Sets.- 1.3 Notation for Sets.- 1.4 Sets of Sets.- 1.5 Relations.- 1.6 Functions.- 1.7 Well-Or der ings and Ordinals.- 1.8 Problems.- 2 The Zermelo—Fraenkel Axioms.- 2.1 The Language of Set Theory.- 2.2 The Cumulative Hierarchy of Sets.- 2.3 The Zermelo—Fraenkel Axioms.- 2.4 Classes.- 2.5 Set Theory as an Axiomatic Theory.- 2.6 The Recursion Principle.- 2.7 The Axiom of Choice.- 2.8 Problems.- 3 Ordinal and Cardinal Numbers.- 3.1 Ordinal Numbers.- 3.2 Addition of Ordinals.- 3.3 Multiplication of Ordinals.- 3.4 Sequences of Ordinals.- 3.5 Ordinal Exponentiation.- 3.6 Cardinality, Cardinal Numbers.- 3.7 Arithmetic of Cardinal Numbers.- 3.8 Regular and Singular Cardinals.- 3.9 Cardinal Exponentiation.- 3.10 Inaccessible Cardinals.- 3.11 Problems.- 4 Topics in Pure Set Theory.- 4.1 The Borel Hierarchy.- 4.2 Closed Unbounded Sets.- 4.3 Stationary Sets and Regressive Functions.- 4.4 Trees.- 4.5 Extensions of Lebesgue Measure.- 4.6 A Result About the GCH.- 5 The Axiom of Constructibility.- 5.1 Constructible Sets.- 5.2 The Constructible Hierarchy.- 5.3 The Axiom of Constructibility.- 5.4 The Consistency of V = L.- 5.5 Use of the Axiom of Constructibility.- 6 Independence Proofs in Set Theory.- 6.1 Some Undecidable Statements.- 6.2 The Idea of a Boolean-Valued Universe.- 6.3 The Boolean-Valued Universe.- 6.4 VB and V.- 6.5 Boolean-Valued Sets and Independence Proofs.- 6.6 The Nonprovability of the CH.- 7 Non-Well-Founded Set Theory.- 7.1 Set-Membership Diagrams.- 7.2 The Anti-Foundation Axiom.- 7.3 The Solution Lemma.- 7.4 Inductive Definitions Under AFA.- 7.5 Graphs and Systems.- 7.6 Proof of the Solution Lemma.- 7.7 Co-Inductive Definitions.- 7.8 A Model of ZF- +AFA.- Glossary of Symbols.