| Description |
1 online resource (353 pages) |
| Series |
London Mathematical Society lecture note series ; 47 |
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London Mathematical Society lecture note series ; 47.
|
| Contents |
Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA |
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3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 ÔAND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0̂; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets |
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8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index |
| Summary |
Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account |
| Bibliography |
Includes bibliographical references (pages 347-348) |
| Notes |
Includes indexes |
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Print version record |
| Subject |
Axiomatic set theory.
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Logic, Symbolic and mathematical.
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MATHEMATICS -- Set Theory.
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Axiomatic set theory
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Logic, Symbolic and mathematical
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Zermelo-Fraenkel-Axiome
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Axiomatische methode.
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Symbolische logica.
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| Form |
Electronic book
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| Author |
Jensen, Ronald Björn
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Welch, P
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| ISBN |
9781107361058 |
|
1107361052 |
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9780511892042 |
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0511892047 |
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