ENGLISH

Classical Set Theory: Theory of Sets and Classes

By Taras Banakh

Book information

Year
2020
Language
english
Format
PDF
Filesize
1 MB (1376834 bytes)
Pages
162\162
Time added
2021-12-19 11:44:38

Description

Introduction Part 1. Naive Set Theory 1. Origins of Set Theory 2. Berry's Paradox 3. The language and formulas of Set Theory 4. Russell's Paradox Part 2. Axiomatic Theories of Sets 5. Axioms of von Neumann–Bernays–Gödel 6. Existence of Classes 7. Gödel's Theorem on class existence 8. Axiomatic Set Theory of Zermelo–Fraenkel Part 3. Fundamental Constructions 9. Cartesian products of sets 10. Relations 11. Functions 12. Indexed families of classes 13. Cartesian products of classes 14. Reflexive and irreflexive relations 15. Equivalence relations 16. Well-Founded relations Part 4. Order 17. Order relations 18. Transitivity 19. Ordinals 20. Trees 21. Recursion Theorem 22. Ranks 23. Well-orders Part 5. Foundation and Constructibility 24. Foundation 25. Constructibility 26. Inner Models Part 6. Choice and Global Choice 27. Choice 28. Global Choice Part 7. Ordinal Arithmetics 29. Transfinite Dynamics 30. Successors 31. Addition 32. Multiplication 33. Exponentiation 34. Cantor's normal form Part 8. Cardinals 35. Cardinalities and cardinals 36. Finite and Countable sets 37. Successor cardinals and alephs 38. Arithmetics of Cardinals 39. Cofinality of cardinals 40. (Generalized) Continuum Hypothesis 41. Inaccessible and measurable cardinals Part 9. Linear orders 42. Completeness 43. Universality 44. Cuts 45. Gaps Part 10. Numbers 46. Integer numbers 47. Rational numbers 48. Real numbers 49. Surreal numbers Part 11. Mathematical Structures 50. Examples of Mathematical Structures 51. Morphisms of Mathematical Structures 52. A characterization of the real line Part 12. Elements of Category Theory 53. Categories 54. Functors 55. Natural transformations 56. Skeleta and equivalence of categories 57. Limits and colimits 57.1. Products and coproducts 57.2. Pullbacks and pushouts 57.3. Equalizers and coequalizers 57.4. Limits and colimits of diagrams 58. Characterizations of the category Set 59. Cartesian closed categories 60. Subobject classifiers 61. Elementary Topoi Epilogue References

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