Language:
שפה נוכחית
Surveys in set theory
Enlarge text Shrink text- Book
This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.
| Title |
Surveys in set theory / edited by A.R.D. Mathias. |
|---|---|
| Publisher |
Cambridge [Cambridgeshire] New York : Cambridge University Press |
| Creation Date |
1983 |
| Notes |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). Includes bibliographical references. English |
| Content |
Cover Title Copyright Contents PREFACE ITERATED FORCING 0. Introduction and terminology 1. Iterated forcing 2. Chain conditions and closure 3. Martin's Axiom 4. Generalized Martin's Axiom 5. Intermediate Stages 6. Reverse Easton Forcing 7. Axiom A forcing 8. An application to trees 9. Iterated Mathias forcing and the Borel Conjecture References THE YORKSHIREMAN'S GUIDE TO PROPER FORCING 0. INTRODUCTION 1. PRELIMINARIES 3. PROPER ITERATIONS 4. COLORING LADDER SYSTEMS 5. THE PROPER FORCING AXIOM 6. HISTORICAL REMARKS THE SINGULAR CARDINALS PROBLEM INDEPENDENCE RESULTSAbstract Notation Notation on forcing 1 1.1. Framework 1.2 The forcing notion 1.3 Technical Definitions on the forcing conditions 1.4 The Inner Model 1.5 Automorphism of P 1.6 Claim 1.7 Definition. Good Cardinals for P 1.8 The Main Lemma 1.9. Notation 1.10. Claim 1.11. Claim 1.12 Proof of the Main Lemma 1.8B 1.13 Claim 1.14. Corollary 1.15 Claim 2. Applications REFERENCES TREES, NORMS AND SCALES 0. Introduction 1. Trees 2. Norms 3. Scales ON THE REGULARITY OF ULTRAFILTERS MORASSES IN COMBINATORIAL SET THEORY 1. PRIKRY'S PRINCIPLE2. SILVER'S PRINCIPLE 3. BURGESS' PRINCIPLE 4. GENERALIZATIONS A SHORT COURSE ON GAP-ONE MORASSES WITH A REVIEW OF THE FINE STRUCTURE OF L 1. Introduction 2 THE FINE STRUCTURE OF L, NOW THAT THE DUST HAS CLEARED 3 MORASSES AND CONSTRUCTING THEM IN L 4. COMBINATORIAL APPLICATIONS 5. GETTING MORASSES BY FORCING LIST OF PARTICIPANTS |
| Series |
London Mathematical Society lecture note series 87 |
| Extent |
1 online resource (247 pages) : digital, PDF file(s). |
| Language |
English |
| National Library system number |
997010714014005171 |
MARC RECORDS
Have more information? Found a mistake?
