Set Theory and Its Logic
by Quine, W. V.Edition: Revised
Format: Paperback
Pub. Date: 2000-05-05
Publisher(s): Belknap Pr
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Summary
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Table of Contents
| Introduction | |
| The Elements | |
| Logic Quantification and identity Virtual Classes Virtual relations | |
| Real Classes Reality, extensionality, and The individual The virtual Amid The real Identity and substitution | |
| Classes of Classes Unit Classes Unions, intersections, descriptions Relations As Classes of pairs Functions | |
| Natural Numbers Numbers unconstrued Numbers construed Induction | |
| Iteration and Arithmetic Sequences and iterates The Ancestral Sum, product, power | |
| Higher Forms of Number | |
| Real Numbers Program. | |
| Numerical pairs Ratios and reals construed Existential needs. | |
| Operations and extensions | |
| Order and Ordinals Transfinite induction | |
| Order Ordinal numbers Laws of ordinals | |
| The order of The ordinals | |
| Transfinite Recursion | |
| Transfinite recursion Laws of Transfinite recursion Enumeration | |
| Cardinal Numbers Comparative size of Classes | |
| The SchrOder-Bernstein | |
| Theorem Infinite cardinal numbers | |
| The Axiom of Choice Selections and selectors | |
| Further equivalents of The Axiom | |
| The place of The Axiom | |
| Axiom Systems | |
| Russell'S Theory of Types | |
| The constructive part Classes and The Axiom of reducibility | |
| The modern Theory of types | |
| General Variables and Zermelo | |
| The Theory of types with general variables | |
| Cumulative types and Zermelo Axioms of infinity and Others | |
| Stratification and Ultimate Classes "New foundations" Non-Cantorian Classes. | |
| Induction Again Ultimate Classes Added | |
| Von Neumann'S System and Others | |
| The von Neumann-Bernays system Departures and comparisons Strength of systems | |
| Synopsis of Five Axiom Systems List of Numbered Formulas | |
| Bibliographical | |
| References | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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