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Set theory : an introduction to large cardinals / Frank R. Drake

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Studies in logic and the foundations of mathematics ; v. 76Publisher: Amsterdam ; New York : North-Holland Pub. Co, 2011Description: Online Ressource (xii, 351 pages)ISBN:
  • 9780444105356
  • 9780080954868
  • 0080954863
  • 0444105352
  • 0720422000
  • 0720422795
  • 9780444105356
  • 9780720422009
  • 9780720422795
Subject(s): Additional physical formats: 0444105352 | 0720422000 | 0720422795 | Erscheint auch als: Set theory. Druck-Ausgabe Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co, 1974DDC classification:
  • 512.72
RVK: RVK: SK 150 | SK 130LOC classification:
  • QA248
Online resources: Additional physical formats: Online-Ausg. [S.l.] : HathiTrust Digital LibrarySummary: 1. pai nm and Sigma nm-indescribables2. Enforceable classes; 3. Indescribability of measurable cardinals; 4. v-indescribable cardinals; Notes to Chapter 9; Chapter 10. Infinitarylanguages and Large Cardinals; 1. The languages Laß; 2. Weakly compact cardinals; 3. Strongly compact cardinals; 4. Summary of large cardinals; Notes to Chapter 10; Bibliography; Index; List of Symbols and Abbreviations Used and Page Where IntroducedSummary: 7. The generalized continuum hypothesis inaccessible cardinals; 8. Ramsey's theorem; Notes to Chapter 2; Chapter 3. The Lévy Hierarchy And The Reflection Principle; 1. Transitive €-structures; 2. Lévy's hierarchy; 3. Delta and transfinite induction; 4. Absoluteness; 5. Delta-definability of the satisfaction relation; 6. The reflection principle of ZF; 7. Cardinality and Sigma-formulas; Notes to Chapter 3; Chapter 4. Inaccessible and Mahlocardinals; 1. Properties of Va; 2. Normal functions; 3. Mahlo cardinals; 4. Reflection principles for Mahlo cardinals; Notes to Chapter 4Summary: Chapter 5. The Constructible Universe1. Constructible sets; 2. Gödel's theorems on L: AC and GCH; 3. Constructible orders; 4. On reducing proofs to ZFC; 5. The minimal model of ZF; 6. Relative constructibility; 7. The analytical hierarchy and constructible sets; 8. Ordinal definable sets; Notes to Chapter 5; Chapter 6. Measurable Cardinals; 1. Measures: classical properties; 2. The ultrapower construction for measurable cardinals; 3. Normal measures; 4. Measurable cardinals and constructible sets; 5. Measurable cardinals and the GCH; Notes to Chapter 6Summary: Front Cover; Set Theory: An Introduction to Large Cardinals; Copyright Page; Contents; Preface; Chapter 1. Introduction: Sets and Languages; 1. What are sets?-The cumulative type structure; 2. The first-order language of set theory; 3. The Zermelo-Fraenkel axioms; 4. A note on paradoxes; 5. More general languages; 6. The hereditarily finite sets-an example; Notes to Chapter 1; Chapter 2. Thedevelopment of ZFC; 1. Elementary definitions; 2. Ordinals; 3. Transfinite induction; 4. Cardinals: introduction; 5. Cardinal arithmetic; 6. The axiom of choiceSummary: Provability, Computability and ReflectionPPN: PPN: 878888454Package identifier: Produktsigel: BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
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Online-Ausg. [S.l.] : HathiTrust Digital Library

Online-Ausg. [S.l.] : HathiTrust Digital Library. Online-Ausg. [S.l.] : HathiTrust Digital Library

Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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