Set Theory and Its Logic, Revised Edition
Revised Edition
1st Edition
Published on 30. June 2009
381 pages
978-0-674-04242-1 (ISBN)
Description
This is an extensively revised edition of W. V. 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.
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W. V. Quine
Set Theory and Its Logic
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Content
- Intro
- Contents
- Introduction
- Part One. The Elements
- I. Logic
- 1. Quantification and identity
- 2. Virtual classes
- 3. Virtual relations
- II. Real Classes
- 4. Reality, extensionality, and the individual
- 5. The virtual amid the real
- 6. Identity and substitution
- III. Classes of Classes
- 7. Unit classes
- 8. Unions, intersections, descriptions
- 9. Relations as classes of pairs
- 10. Functions
- IV. Natural Numbers
- 11. Numbers unconstrued
- 12. Numbers construed
- 13. Induction
- V. Iteration and Arithmetic
- 14. Sequences and iterates
- 15. The ancestral
- 16. Sum, product, power
- Part Two. Higher Forms of Number
- VI. Real Numbers
- 17. Program. Numerical pairs
- 18. Ratios and reaIs construed
- 19. Existential needs. Operations and extensions
- VII. Order and Ordinals
- 20. Transfinite induction
- 21. Order
- 22. Ordinal numbers
- 23. Laws of ordinals
- 24. The order of the ordinals
- VIII. Transfinite Recursion
- 25. Transfinite recursion
- 26. Laws of transfinite recursion
- 27. Enumeration
- IX. Cardinal Numbers
- 28. Comparative size of classes
- 29. The Schröder-Bernstein theorem
- 30. Infinite cardinal numbers
- X. The Axium of Choice
- 31. Selections and selectors
- 32. Further equivalents of the axiom
- 33. The place of the axiom
- Part Three. Axiom Systems
- XI. Russell's Theory of Types
- 34. The constructive part
- 35. Classes and the axiom of reducibility
- 36. The modern theory of types
- XII. General Variables and Zermelo
- 37. The theory of types with general variables
- 38. Cumulative types and Zermelo
- 39. Axioms of infinity and others
- XIII. Stratification and Ultimate Classes
- 40. "New foundations"
- 41. Non-Cantorian classes. Induction again
- 42. Ultimate classes added
- XIV. Von Neumann's System and Others
- 43. The von Neumann-Bernays system
- 44. Departures and comparisons
- 45. Strength of systems
- Synopsis of Five Systems
- List of Numbered Formulas
- Bibliographical References
- Index
