Introduction to set theory

Preface......Page f007.djvu
Contents......Page f009.djvu
Introduction: Intuitive logic......Page p001.djvu
1 The axioms......Page p012.djvu
2 Boolean algebra of classes......Page p013.djvu
3 Algebra of relations......Page p024.djvu
4 Functions......Page p040.djvu
5 Infinite Boolean operations......Page p049.djvu
6 Direct products, power classes......Page p055.djvu
7 Equivalence relations......Page p057.djvu
8 Ordering......Page p061.djvu
9 Ordinals: basic properties......Page p068.djvu
10 Transfinite induction......Page p075.djvu
11 The natural numbers......Page p078.djvu
12 Sequences and normal functions......Page p081.djvu
13 Recursion......Page p086.djvu
14 Ordinal arithmetic......Page p097.djvu
15 Special topics......Page p105.djvu
16 Equivalents of the axiom of choice......Page p116.djvu
17 Applications of the axiom of choice......Page p122.djvu
18 Cardinals: basic definitions......Page p129.djvu
19 Finite and infinite sets......Page p134.djvu
20 Cardinal addition......Page p137.djvu
21 Cardinal multiplication......Page p141.djvu
22 Cardinal exponentiation......Page p150.djvu
23 Regular and singular cardinals......Page p155.djvu
24 Applications......Page p163.djvu
Appendix: Axiomatic logic......Page p168.djvu
Axioms of set theory......Page p180.djvu
Bibliography......Page p181.djvu
Index of notations......Page p185.djvu
Subject Index......Page p189.djvu