Coding the universe / A. Beller, R. Jensen, P. Welch.

Format:

Book

Author/Creator:

Beller, A., author.

Jensen, Ronald Björn, author.

Welch, P., author.

Series:

London Mathematical Society lecture note series ; 47.

London Mathematical Society lecture note series ; 47

Language:

English

Subjects (All):

Axiomatic set theory.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (353 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1982.

Language Note:

English

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.

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

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 O^AND 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 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets

8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Bibliography: p. 347-348.

ISBN:

1-139-88160-4

1-107-36596-1

1-107-37069-8

1-107-36105-2

0-511-95945-1

1-299-40377-8

1-107-36350-0

0-511-89204-7

0-511-62919-2