Set theory : an introduction to independence proofs / Kenneth Kunen.

Format:

Book

Author/Creator:

Kunen, Kenneth.

Contributor:

ScienceDirect (Online service)

Series:

Studies in logic and the foundations of mathematics ; v. 102.

Studies in logic and the foundations of mathematics ; v. 102

Language:

English

Subjects (All):

Axiomatic set theory.

Physical Description:

1 online resource (xvi, 313 pages.)

Place of Publication:

Amsterdam ; New York : North-Holland Pub. Co. ; New York : Sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1980.

System Details:

text file

Contents:

1 Consistency results xi

5 What has been omitted xiv

7 The axioms xv

Chapter I The foundations of set theory 1

1 Why axioms? 1

2 Why formal logic? 2

3 The philosophy of mathematics 6

4 What we are describing 8

5 Extensionality and Comprehension 10

6 Relations, functions, and well-ordering 12

7 Ordinals 16

8 Remarks on defined notions 22

9 Classes and recursion 23

10 Cardinals 27

11 The real numbers 35

12 Appendix 1: Other set theories 35

13 Appendix 2: Eliminating defined notions 36

14 Appendix 3: Formalizing the metatheory 38

Chapter II Infinitary combinatorics 47

1 Almost disjoint and quasi-disjoint sets 47

2 Martin's Axiom 51

3 Equivalents of MA 62

4 The Suslin problem 66

5 Trees 68

6 The c.u.b. filter 76

7 [characters not reproducible] and [characters not reproducible] 80

Chapter III The well-founded sets 94

2 Properties of the well-founded sets 95

3 Well-founded relations 98

4 The Axiom of Foundation 100

5 Induction and recursion on well-founded relations 102

Chapter IV Easy consistency proofs 110

1 Three informal proofs 110

2 Relativization 112

3 Absoluteness 117

4 The last word on Foundation 124

5 More absoluteness 125

6 The H([kappa]) 130

7 Reflection theorems 133

8 Appendix 1: More on relativization 141

9 Appendix 2: Model theory in the metatheory 142

10 Appendix 3: Model theory in the formal theory 143

Chapter V Defining definability 152

1 Formalizing definability 153

2 Ordinal definable sets 157

Chapter VI The constructible sets 165

1 Basic properties of L 165

2 ZF in L 169

3 The Axiom of Constructibility 170

4 AC and GCH in L 173

5 [characters not reproducible] and [characters not reproducible] in L 177

Chapter VII Forcing 184

2 Generic extensions 186

3 Forcing 192

4 ZFC in M[G] 201

5 Forcing with finite partial functions 204

6 Forcing with partial functions of larger cardinality 211

7 Embeddings, isomorphisms, and Boolean-valued models 217

8 Further results 226

9 Appendix: Other approaches and historical remarks 232

Chapter VIII Iterated forcing 251

1 Products 252

2 More on the Cohen model 255

3 The independence of Kurepa's Hypothesis 259

4 Easton forcing 262

5 General iterated forcing 268

6 The consistency of MA + [not sign]CH 278

7 Countable iterations 281.

Notes:

Includes bibliographical references (pages 305-308).

Includes indexes.

Electronic reproduction. Amsterdam Available via World Wide Web.

Description based on print version record.

ISBN:

9780080955087

0080955088

Publisher Number:

99985978674

Access Restriction:

Restricted for use by site license.