Equivalents of the Axiom of Choice, II (eBook)

H. Rubin, J.E. Rubin (Autoren)

eBook Download: PDF

1985 | 1. Auflage
321 Seiten
Elsevier Science (Verlag)
978-0-08-088765-4 (ISBN)

Infos

This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles.

Inhalt

Front Cover 1
Equivalents of the Axiom of Choice, II 4
Copyright Page 5
Preface (1963 Edition) 8
Preface (1985 Edition) 10
Table of Contents 12
Introduction 14
Preliminary Definitions And Theorems 18
Part I: Set Forms 32
Chapter 1. The Well-Ordering Theorem 32
Chapter 2. The Axiom of Choice 38
Chapter 3. The Law of the Trichotomy 52
Chapter 4. Maximal Principles 62
Chapter 5. Forms Equivalent to the Axiom of Choice Under the Axioms of Extensionality and Foundation 104
Chapter 6. Algebraic Forms 124
Chapter 7. Cardinal Number Forms 168
Chapter 8. Forms from Topology, Analysis and Logic 194
Part II: Class Forms 216
Chapter 1. The Well-Ordering Theorem 218
Chapter 2. The Axiom of Choice 222
Chapter 3. Maximal Principles 234
List of the Set Forms 278
List of the Class Forms 302
List of Forms Related to the Axiom of Choice 310
Bibliography 320
Index of Authors 336
Index of Symbols 342
Index of Technical Terms 346

Produkt-Details

• Erscheint lt. Verlag: 1.3.1985
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-088765-1 / 0080887651
• ISBN-13: 978-0-08-088765-4 / 9780080887654