Learn · Set Theory and Mathematical Logic

Lecture 14 of 51week-04

Lecture 14 - Cardinal Numbers and Cardinal Arithmetic

Prof. Amit Kuber · IIT Kanpur

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Set Theory and Mathematical Logic, IIT Kanpur (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures

  1. Lecture 01: Introduction to Set Theory Video
  2. Lecture 02: Operations on Sets, and Functions Video
  3. Lecture 03: Bijective Functions Video
  4. Lecture 04: Equivalence Relations and Partitions Video
  5. Lecture 05: Cantor-Schroder-Bernstein Theorem Video
  6. Lecture 06: Natural Numbers in ZF Set Theory Video
  7. Lecture 07: Standard number systems in ZF set theory Video
  8. Lecture 08: (Finitary) power sets and countability Video
  9. Lecture 09: Bijections of the set of real numbers: Dedekind cut and Cantor’s middle-third set Video
  10. Lecture 10: Bijections of the set of real numbers: Continued Fractions Video
  11. Lecture 11 - Principles of Mathematical Induction Video
  12. Lecture 12 - Ordinal Numbers Video
  13. Lecture 13 - Ordinal Arithmetic Video
  14. Lecture 14 - Cardinal Numbers and Cardinal Arithmetic Video
  15. Lecture Tutorial - Week 4 Video
  16. Lecture 15 - Partial Orders Video
  17. Lecture 16 - Lattices Video
  18. Lec 17 - Equivalents of the Axiom of Choice (AC): Zorn's Lemma (ZL) and Well-ordering theorem (WOT) Video
  19. Lecture Tutorial - Week 5 Video
  20. Lecture 18 - Boolean Algebras Video
  21. Lecture 19 - Stone's Representation Theorems for Boolean Algebras Video
  22. Lecture 20 - Some Exercises on Boolean Algebras Video
  23. Lecture 21 - Ultrafilters in Boolean Algebras Video
  24. Lecture 22 - Introduction to Mathematical Logic Video
  25. Lecture 23 - Propositional Logic: Language, Formulas and Valuations Video
  26. Lecture 24 - Propositional Logic: Logical Equivalence and Lindenbaum-Tarski Algebra Video
  27. Tutorial : Week 07 Video
  28. Lecture 25 - Propositional Logic: Normal Forms of Formulas and Adequacy of Connectives Video
  29. Lecture 26 - Propositional Logic: Semantic Consequence Relation Video
  30. Lecture 27 - Propositional Logic: Syntactic Consequence Relation Video
  31. Lecture 28 - Deduction Theorem (Continued...) Video
  32. Lecture Tutorial : Week 08 Video
  33. Lecture 29 - Propositional Logic: Consistency and Soundness Theorem Video
  34. Lecture 30 - Propositional Logic: Completeness Theorem - Part I Video
  35. Lecture 31 - Propositional Logic: Completeness Theorem - Part II Video
  36. Lecture 32 - Compactness Theorem and Konig's Lemma Video
  37. Lecture Tutorial : Week 09 Video
  38. Lecture 33 - Introduction to First-Order Predicate Logic Video
  39. Lecture 34 - Predicate Logic: Terms and Formulas Video
  40. Lecture 35 - Predicate Logic: Validity of Formulas Video
  41. Lecture Tutorial : Week 10 Video
  42. Lecture 36 - Predicate Logic Substructures, Semantic Consequence Relation, and Models of Theories Video
  43. Lecture 37 - Predicate Logic: Standard Logical Equivalences, Normal Forms, and Definable Sets Video
  44. Lecture Tutorial : Week 11 Video
  45. Lecture 38 - Hyperreal Numbers Video
  46. Lecture 39 - Predicate Logic: Ultraproduct of Structures and Los's Theorem Video
  47. Lecture 40 - Predicate Logic: Compactness Theorem Video
  48. Lecture Tutorial : Week 12 Video
  49. Live Session 21-02-2024 Video
  50. Live Session 23-03-2024 Video
  51. Live Session 26-04-2025 Video