Set theory and its logic /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Quine, W. V. (Willard Van Orman)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, Mass. : Belknap Press of Harvard University Press, 1969.
Edición:Rev. ed.
Temas:
Axiomatic set theory.
Logic, Symbolic and mathematical.
Théorie axiomatique des ensembles.
Logique symbolique et mathématique.
MATHEMATICS > Algebra > Intermediate.
PHILOSOPHY > Logic.
Axiomatic set theory
Logic, Symbolic and mathematical
Acceso en línea:Texto completo
Tabla de Contenidos:
  • PREFACE TO THE REVISED EDITION
  • PREFACE TO THE FIRST EDITION
  • 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 construed13. 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 recursion27. Enumeration
  • IX. CARDINAL NUMBERS
  • 28. Comparative size of classes
  • 29. The SchrÃœder-Bernstein theorem
  • 30. Infinite cardinal numbers
  • X. THE AXIOM OF CHOICE
  • 31. Selections and selectors
  • 32. Further equivalents of the axiom
  • 33. The place of the axiom
  • Part Three. Axiom Systems
  • XI. RUSSELLâ€?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 variables38. Cumulative types and Zermelo
  • 39. Axioms of infinity and others
  • XIII. STRATIFICATION AND ULTIMATE CLASSES
  • 40. “New foundationsâ€?
  • 41. Non-Cantorian classes. Induction again
  • 42. Ultimate classes added
  • XIV. VON NEUMANNâ€?S SYSTEM AND OTHERS
  • 43. The von Neumannâ€?Bernays system
  • 44. Departures and comparisons
  • 45. Strength of systems
  • SYNOPSIS OF FIVE AXIOM SYSTEMS
  • LIST OF NUMBERED FORMULAS
  • BIBLIOGRAPHICAL REFERENCES
  • INDEX

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