Sold Out
Book Categories |
Preface | ||
Pt. I | Introduction to set theory | 1 |
1 | Notation, conventions | 5 |
2 | Definition of equivalence. The concept of cardinality. The Axiom of Choice | 11 |
3 | Countable cardinal, continuum cardinal | 15 |
4 | Comparison of cardinals | 21 |
5 | Operations with sets and cardinals | 28 |
6 | Examples | 36 |
7 | Ordered sets. Order types. Ordinals | 41 |
8 | Properties of wellordered sets. Good sets. The ordinal operation | 54 |
9 | Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem | 66 |
10 | Definition of the cardinality operation. Properties of cardinalities. The cofinality operation | 77 |
11 | Properties of the power operation | 93 |
App | An axiomatic development of set theory | 107 |
A1 | The Zermelo-Fraenkel axiom system of set theory | 111 |
A2 | Definition of concepts; extension of the language | 114 |
A3 | A sketch of the development. Metatheorems | 117 |
A4 | A sketch of the development. Definitions of simple operations and properties (continued) | 122 |
A5 | A sketch of the development. Basic theorems, the introduction of [omega] and R (continued) | 124 |
A6 | The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 | 128 |
A7 | The role of the Axiom of Regularity | 130 |
A8 | Proofs of relative consistency. The method of interpretation | 133 |
A9 | Proofs of relative consistency. The method of models | 138 |
Pt. II | Topics in combinatorial set theory | 143 |
12 | Stationary sets | 145 |
13 | [Delta]-systems | 159 |
14 | Ramsey's Theorem and its generalizations. Partition calculus | 164 |
15 | Inaccessible cardinals. Mahlo cardinals | 184 |
16 | Measurable cardinals | 190 |
17 | Real-valued measurable cardinals, saturated ideals | 203 |
18 | Weakly compact and Ramsey cardinals | 216 |
19 | Set mappings | 228 |
20 | The square-bracket symbol. Strengthenings of the Ramsey counterexamples | 234 |
21 | Properties of the power operation. Results on the singular cardinal problem | 243 |
22 | Powers of singular cardinals. Shelah's Theorem | 259 |
Bibliography | 295 | |
List of symbols | 297 | |
Name index | 301 | |
Subject index | 303 |
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionSet Theory
X
This Item is in Your InventorySet Theory
X
You must be logged in to review the productsX
X
X
Add Set Theory, , Set Theory to the inventory that you are selling on WonderClubX
X
Add Set Theory, , Set Theory to your collection on WonderClub |