Set Theory
An Introduction to Large Cardinals
Published on 14. May 2014
365 pages
978-0-08-095486-8 (ISBN)
Description
Set Theory
More details
Series
Language
English
Place of publication
Burlington
Netherlands
ISBN-13
978-0-08-095486-8 (9780080954868)
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Schweitzer Classification
Other editions
Additional editions
Lev D. Beklemishev
Provability, Computability and Reflection: Volume 76
Book
04/2000
Elsevier
€210.46
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Content
- 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
