Set Theory

Name: Set Theory | An Introduction to Large Cardinals
Brand: Elsevier
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An Introduction to Large Cardinals

F. R. Drake Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

365 Seiten

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Inhalt

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 choice
§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 4
Chapter 5. The Constructible Universe
§1. 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 6
Chapter 7. Trees and Partition Properties
§1. Trees
§2. Generalizations of Ramsey's theorem
§3. Partition cardinals: K ( K )squre
§4. Partition cardinals: K (a)&w
§5. Souslin and Kurepa trees
Notes to Chapter 7
Chapter 8. Partition Cardinals and Model Theory: Silver's Results
§1. Indiscernibles in a structure
§2. K (a)&w and indiscernibles
§3. Constructing models using indiscernibles
§4. Implications for the constructible universe
§5. A delta non-constructible set
§6. Further properties of Lµ
Notes to Chapter 8
Chapter 9.Indescribable Cardinals
§1. pai nm and Sigma nm-indescribables
§2. 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 Introduced

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