Abstract Set Theory

Title ......Page 1
Copyright ......Page 2
Preface ......Page 3
Contents ......Page 4
1. Historical remarks. Outlines of Cantor\'s theory ......Page 5
2. Ordered sets. A theorem of Hausdorff ......Page 11
3. Axiomatic set theory. Axioms of Zermelo and Fraenkel ......Page 16
4. The well-ordering theorem ......Page 23
5. Ordinals and alephs ......Page 26
6. Some remarks on functions of ordinal numbers ......Page 32
7. On the exponentiation of alephs ......Page 36
8. Sets representing ordinals ......Page 39
9. The notions \"finite\" and \"infinite\" ......Page 42
10. The simple infinite sequence. Development of arithmetic ......Page 45
11. Some remarks on the nature of the set-theoretic axioms. The Contents set-theoretic relativism ......Page 49
12. The simple theory of types ......Page 52
13. The theory of Quine ......Page 54
14. The ramified theory of types. Predicative set theory ......Page 56
15. Lorenzen\'s operative mathematics ......Page 65
16. Some remarks on intuitionist mathematics ......Page 68
17. Mathematics without quantifiers ......Page 72
18. The possibility of set theory based on many-valued logic ......Page 73