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《21. Set Theory. Finite Sets》
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英字【集合论】加州伯克利大学 Set Theory | MATH-135 (Antonio Montalban)
https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf
下载列表:共53讲
- 1. Introduction to Mathematical Logic
- 2. Set Theory. Basic concepts
- 3. Set Theory. First Five Axioms
- 4. Set Theory. The Union Axiom
- 5. Set Theory. The Subset Axiom
- 6. Set Theory. The Language of First-Order Logic
- 7. Set Theory. Order Pairs in set theory
- 8. Set Theory. Relations in set theory
- 9. Set Theory. Functions
- 10. Set Theory. Equivalence Relations
- 11. Set Theory. Infinite Cartesian Products
- 12. Set Theory. The Model Of Hereditarily Finite Sets
- 13. Set Theory. Natural Numbers
- 14. Set Theory. Induction on the Natural Numbers
- 15. Set Theory. Transitive Sets
- 16. Set Theory. Recursion and Arithmetic
- 17. Set Theory - Integers
- 18. Set Theory - Rational Numbers
- 19. Set Theory. Real Numbers
- 19. Set Theory. Equinumerosity
- 20. Set Theory. Cantors diagonal argument
- 21. Set Theory. Finite Sets
- 22. Set Theory. Cardinality
- 23. Set Theory. Cardinal arithmetic
- 24. Set Theory. Ordering cardinals
- 25. Set Theory. Infinite sets dominate omega
- 26. Set Theory. The Shroder--Bernstein Theorem
- 27. Set Theory. Comparability of Cardinals
- 28. Set Theory. Version of the Axiom Of Choice
- 29. Set Theory. Every Vector Space has a basis using AC
- 30. Set Theory. There is no measure on all sets of reals
- 32. Set Theory. Comparing cardinals via onto functions
- 33. Set Theory. Countable Sets
- 34. Set Theory. Absorption law of cardinal arithmetic
- 35. Set Theory. Multiplication of infinite cardinals
- 36. Set Theory. The continuum hypothesis
- 37. Set Theory. Well orderings
- 38. Set Theory. Transfinite Induction
- 39. Set Theory. Transfinite Recursion
- 40. Set Theory. Replacement Axiom
- 41. Set theory. A proof of Transfinite Recursion
- 42. Set Theory. Epsilon Images
- 43. Set Theory. Ordinals
- 44. Set Theory. Comparability of Ordinals
- 45. Set Theory. The Burali-Forti paradox
- 46. Set Theory. Hartog's Theorem
- 47. Set Theory. A Proof of Zorn's Lemma
- 48. Finishing the proof of equivalent versions of the Axiom of Choice
- 49. Set Theory. The V hierarchy
- 50. Set Theory. Regularity Axiom
- 51. Cardinals As Ordinals
- 52. Set Theory. Alephs
- Set Theory - Determinacy of infinite games
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