Basic set theory / A. Shen, N.K. Vereshchagin.

Format:

Book

Author/Creator:

Shen, A. (Alexander), 1958-

Contributor:

Vereshchagin, Nikolai Konstantinovich, 1958-

Series:

Student mathematical library 1520-9121 ; v. 17.

Student mathematical library, 1520-9121 ; v. 17

Standardized Title:

Osnovy teorii mnozhestv. English

Language:

English

Russian

Subjects (All):

Set theory.

Physical Description:

viii, 116 pages : illustrations ; 22 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2002]

Contents:

Chapter 1. Sets and Their Cardinalities 1

1. Sets 1

2. Cardinality 4

3. Equal cardinalities 7

4. Countable sets 9

5. Cantor-Bernstein Theorem 16

6. Cantor's Theorem 24

7. Functions 30

8. Operations on cardinals 35

Chapter 2. Ordered Sets 41

1. Equivalence relations and orderings 41

2. Isomorphisms 47

3. Well-founded orderings 52

4. Well-ordered sets 56

5. Transfinite induction 59

6. Zermelo's Theorem 66

7. Transfinite induction and Hamel basis 69

8. Zorn's Lemma and its application 74

9. Operations on cardinals revisited 78

10. Ordinals 83

11. Ordinal arithmetic 87

12. Recursive definitions and exponentiation 91

13. Application of ordinals 99.

Notes:

Authors' names on t.p. of translation reversed from original.

Includes bibliographical references (pages 109-110) and index.

ISBN:

0821827316

OCLC:

49559026