Book:Gaisi Takeuti/Introduction to Axiomatic Set Theory

Subject Matter

 * Set Theory
 * Inner Model Theory

Contents

 * Preface


 * $\S 1$. Introduction
 * $\S 2$. Language and Logic
 * $\S 3$. Equality
 * $\S 4$. Classes
 * $\S 5$. The Elementary Properties of Classes
 * $5.20$. No Membership Loops
 * $\S 6$. Functions and Relations
 * $6.23$. Foundational Relation has no Relational Loops
 * $6.26$. Well-Founded Relation Determines Minimal Elements/Special Case
 * $6.27$. Well-Founded Induction/Special Case
 * $\S 7$. Ordinal Numbers
 * $7.1$. Definition:Transitive Class
 * $7.2$. Element of Transitive Class
 * $7.3$. Alternate Definition of an Ordinal
 * $7.4$. Alternate Definition of an Ordinal
 * $7.5$. Subset of Ordinals has Minimal Element
 * $7.6$. Initial Segment of Ordinal is Ordinal
 * $7.7$. Ordinal Proper Subset Membership
 * $7.10$. Ordinal Membership Trichotomy
 * $7.11$. Definition:Ordinal Class
 * $7.12$. Ordinal Class is Ordinal
 * $7.14$. Ordinal Member of Ordinal Class
 * $7.15$. Ordinal Subset of Ordinal Class
 * $7.17$. Principle of Transfinite Induction
 * $7.28$. Definition:Minimal Infinite Successor Set
 * $7.40$. Principle of Transfinite Recursion
 * $\S 8$. Ordinal Arithmetic
 * $\S 9$. Relational Closure and the Rank Functions
 * $\S 10$. Cardinal Numbers
 * $\S 11$. The Axiom of Choice, the Greater Continuum Hypothesis, and Cardinal Arithmetic
 * $\S 12$. Models
 * $\S 13$. Absoluteness
 * $\S 14$. The Fundamental Operations
 * $\S 15$. The Gödel Model
 * $\S 16$. The Arithmetization of Model Theory
 * $\S 17$. Cohen's Model
 * $\S 18$. Forcing
 * $\S 19$. Languages, Structures and Models


 * Bibliography


 * Problem List


 * Appendix


 * Index


 * Index of Symbols