# Set Theory and Mathematical Logic

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Amit Kuber
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104416)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104416)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01: Introduction to Set Theory](https://invisiblenetwork.ai/learn/nptel/111104416/58f3aade872c) (Video)
2. [Lecture 02: Operations on Sets, and Functions](https://invisiblenetwork.ai/learn/nptel/111104416/419aa933685d) (Video)
3. [Lecture 03: Bijective Functions](https://invisiblenetwork.ai/learn/nptel/111104416/3ccaa89e5582) (Video)
4. [Lecture 04: Equivalence Relations and Partitions](https://invisiblenetwork.ai/learn/nptel/111104416/febc45cd6fdf) (Video)
5. [Lecture 05: Cantor-Schroder-Bernstein Theorem](https://invisiblenetwork.ai/learn/nptel/111104416/a713bbea09a8) (Video)
6. [Lecture 06: Natural Numbers in ZF Set Theory](https://invisiblenetwork.ai/learn/nptel/111104416/3b7d2be802b6) (Video)
7. [Lecture 07: Standard number systems in ZF set theory](https://invisiblenetwork.ai/learn/nptel/111104416/a2edab4ab50d) (Video)
8. [Lecture 08: (Finitary) power sets and countability](https://invisiblenetwork.ai/learn/nptel/111104416/72c1044c0994) (Video)
9. [Lecture 09: Bijections of the set of real numbers: Dedekind cut and Cantor’s middle-third set](https://invisiblenetwork.ai/learn/nptel/111104416/08129927b2c1) (Video)
10. [Lecture 10: Bijections of the set of real numbers: Continued Fractions](https://invisiblenetwork.ai/learn/nptel/111104416/13ca9b72b676) (Video)
11. [Lecture 11 - Principles of Mathematical Induction](https://invisiblenetwork.ai/learn/nptel/111104416/5c4b9e32bb4f) (Video)
12. [Lecture 12 - Ordinal Numbers](https://invisiblenetwork.ai/learn/nptel/111104416/eb49fd3061ad) (Video)
13. [Lecture 13 - Ordinal Arithmetic](https://invisiblenetwork.ai/learn/nptel/111104416/6eb0f8497410) (Video)
14. [Lecture 14 - Cardinal Numbers and Cardinal Arithmetic](https://invisiblenetwork.ai/learn/nptel/111104416/0dc8653bea84) (Video)
15. [Lecture Tutorial - Week 4](https://invisiblenetwork.ai/learn/nptel/111104416/1e06efee97bd) (Video)
16. [Lecture 15 - Partial Orders](https://invisiblenetwork.ai/learn/nptel/111104416/b69ef65f3845) (Video)
17. [Lecture 16 - Lattices](https://invisiblenetwork.ai/learn/nptel/111104416/d2b966e79873) (Video)
18. [Lec 17 - Equivalents of the Axiom of Choice (AC): Zorn's Lemma (ZL) and Well-ordering theorem (WOT)](https://invisiblenetwork.ai/learn/nptel/111104416/6320631c9959) (Video)
19. [Lecture Tutorial - Week 5](https://invisiblenetwork.ai/learn/nptel/111104416/1b7b96abf757) (Video)
20. [Lecture 18 - Boolean Algebras](https://invisiblenetwork.ai/learn/nptel/111104416/a8e5a3cb62ff) (Video)
21. [Lecture 19 - Stone's Representation Theorems for Boolean Algebras](https://invisiblenetwork.ai/learn/nptel/111104416/920ba7bdbcf1) (Video)
22. [Lecture 20 - Some Exercises on Boolean Algebras](https://invisiblenetwork.ai/learn/nptel/111104416/d854aed33467) (Video)
23. [Lecture 21 - Ultrafilters in Boolean Algebras](https://invisiblenetwork.ai/learn/nptel/111104416/9141404f6015) (Video)
24. [Lecture 22 - Introduction to Mathematical Logic](https://invisiblenetwork.ai/learn/nptel/111104416/6bfd0b15fbae) (Video)
25. [Lecture 23 - Propositional Logic: Language, Formulas and Valuations](https://invisiblenetwork.ai/learn/nptel/111104416/7e717712197b) (Video)
26. [Lecture 24 - Propositional Logic: Logical Equivalence and Lindenbaum-Tarski Algebra](https://invisiblenetwork.ai/learn/nptel/111104416/15cfb7341105) (Video)
27. [Tutorial : Week 07](https://invisiblenetwork.ai/learn/nptel/111104416/077d5f959350) (Video)
28. [Lecture 25 - Propositional Logic: Normal Forms of Formulas and Adequacy of Connectives](https://invisiblenetwork.ai/learn/nptel/111104416/e3244e1a2b24) (Video)
29. [Lecture 26 - Propositional Logic: Semantic Consequence Relation](https://invisiblenetwork.ai/learn/nptel/111104416/a8b4366f016a) (Video)
30. [Lecture 27 - Propositional Logic: Syntactic Consequence Relation](https://invisiblenetwork.ai/learn/nptel/111104416/976e31b4d796) (Video)
31. [Lecture 28 - Deduction Theorem (Continued...)](https://invisiblenetwork.ai/learn/nptel/111104416/419f5d680a5a) (Video)
32. [Lecture Tutorial : Week 08](https://invisiblenetwork.ai/learn/nptel/111104416/d2a3dca6844e) (Video)
33. [Lecture 29 - Propositional Logic: Consistency and Soundness Theorem](https://invisiblenetwork.ai/learn/nptel/111104416/548f55c31bc3) (Video)
34. [Lecture 30 - Propositional Logic: Completeness Theorem - Part I](https://invisiblenetwork.ai/learn/nptel/111104416/db3d10203c0c) (Video)
35. [Lecture 31 - Propositional Logic: Completeness Theorem - Part II](https://invisiblenetwork.ai/learn/nptel/111104416/66bafb766144) (Video)
36. [Lecture 32 - Compactness Theorem and Konig's Lemma](https://invisiblenetwork.ai/learn/nptel/111104416/febfc19989a7) (Video)
37. [Lecture Tutorial : Week 09](https://invisiblenetwork.ai/learn/nptel/111104416/a8f760b7bb7b) (Video)
38. [Lecture 33 - Introduction to First-Order Predicate Logic](https://invisiblenetwork.ai/learn/nptel/111104416/2b5388e8d6c1) (Video)
39. [Lecture 34 - Predicate Logic: Terms and Formulas](https://invisiblenetwork.ai/learn/nptel/111104416/79c8ad068ffc) (Video)
40. [Lecture 35 - Predicate Logic: Validity of Formulas](https://invisiblenetwork.ai/learn/nptel/111104416/84d504242a47) (Video)
41. [Lecture Tutorial : Week 10](https://invisiblenetwork.ai/learn/nptel/111104416/98140db8fbf4) (Video)
42. [Lecture 36 - Predicate Logic Substructures, Semantic Consequence Relation, and Models of Theories](https://invisiblenetwork.ai/learn/nptel/111104416/d82131497e7c) (Video)
43. [Lecture 37 - Predicate Logic: Standard Logical Equivalences, Normal Forms, and Definable Sets](https://invisiblenetwork.ai/learn/nptel/111104416/048387e2e43b) (Video)
44. [Lecture Tutorial : Week 11](https://invisiblenetwork.ai/learn/nptel/111104416/1cdd3d611467) (Video)
45. [Lecture 38 - Hyperreal Numbers](https://invisiblenetwork.ai/learn/nptel/111104416/7d8c0ee93d75) (Video)
46. [Lecture 39 - Predicate Logic: Ultraproduct of Structures and Los's Theorem](https://invisiblenetwork.ai/learn/nptel/111104416/5303b08a5406) (Video)
47. [Lecture 40 - Predicate Logic: Compactness Theorem](https://invisiblenetwork.ai/learn/nptel/111104416/d26fb992c86c) (Video)
48. [Lecture Tutorial : Week 12](https://invisiblenetwork.ai/learn/nptel/111104416/0870cead6d76) (Video)
49. [Live Session 21-02-2024](https://invisiblenetwork.ai/learn/nptel/111104416/58f3aade872c-2) (Video)
50. [Live Session 23-03-2024](https://invisiblenetwork.ai/learn/nptel/111104416/419aa933685d-2) (Video)
51. [Live Session 26-04-2025](https://invisiblenetwork.ai/learn/nptel/111104416/3ccaa89e5582-2) (Video)