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Course11110441651 lectures

Set Theory and Mathematical Logic

Prof. Amit Kuber · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 01: Introduction to Set Theory Video
  2. Lecture 02: Operations on Sets, and Functions Video
  3. Lecture 03: Bijective Functions Video

week-02

  1. Lecture 04: Equivalence Relations and Partitions Video
  2. Lecture 05: Cantor-Schroder-Bernstein Theorem Video
  3. Lecture 06: Natural Numbers in ZF Set Theory Video

week-03

  1. Lecture 07: Standard number systems in ZF set theory Video
  2. Lecture 08: (Finitary) power sets and countability Video
  3. Lecture 09: Bijections of the set of real numbers: Dedekind cut and Cantor’s middle-third set Video
  4. Lecture 10: Bijections of the set of real numbers: Continued Fractions Video

week-04

  1. Lecture 11 - Principles of Mathematical Induction Video
  2. Lecture 12 - Ordinal Numbers Video
  3. Lecture 13 - Ordinal Arithmetic Video
  4. Lecture 14 - Cardinal Numbers and Cardinal Arithmetic Video
  5. Lecture Tutorial - Week 4 Video

week-05

  1. Lecture 15 - Partial Orders Video
  2. Lecture 16 - Lattices Video
  3. Lec 17 - Equivalents of the Axiom of Choice (AC): Zorn's Lemma (ZL) and Well-ordering theorem (WOT) Video
  4. Lecture Tutorial - Week 5 Video

week-06

  1. Lecture 18 - Boolean Algebras Video
  2. Lecture 19 - Stone's Representation Theorems for Boolean Algebras Video
  3. Lecture 20 - Some Exercises on Boolean Algebras Video
  4. Lecture 21 - Ultrafilters in Boolean Algebras Video

week-07

  1. Lecture 22 - Introduction to Mathematical Logic Video
  2. Lecture 23 - Propositional Logic: Language, Formulas and Valuations Video
  3. Lecture 24 - Propositional Logic: Logical Equivalence and Lindenbaum-Tarski Algebra Video
  4. Tutorial : Week 07 Video

week-08

  1. Lecture 25 - Propositional Logic: Normal Forms of Formulas and Adequacy of Connectives Video
  2. Lecture 26 - Propositional Logic: Semantic Consequence Relation Video
  3. Lecture 27 - Propositional Logic: Syntactic Consequence Relation Video
  4. Lecture 28 - Deduction Theorem (Continued...) Video
  5. Lecture Tutorial : Week 08 Video

week-09

  1. Lecture 29 - Propositional Logic: Consistency and Soundness Theorem Video
  2. Lecture 30 - Propositional Logic: Completeness Theorem - Part I Video
  3. Lecture 31 - Propositional Logic: Completeness Theorem - Part II Video
  4. Lecture 32 - Compactness Theorem and Konig's Lemma Video
  5. Lecture Tutorial : Week 09 Video

week-10

  1. Lecture 33 - Introduction to First-Order Predicate Logic Video
  2. Lecture 34 - Predicate Logic: Terms and Formulas Video
  3. Lecture 35 - Predicate Logic: Validity of Formulas Video
  4. Lecture Tutorial : Week 10 Video

week-11

  1. Lecture 36 - Predicate Logic Substructures, Semantic Consequence Relation, and Models of Theories Video
  2. Lecture 37 - Predicate Logic: Standard Logical Equivalences, Normal Forms, and Definable Sets Video
  3. Lecture Tutorial : Week 11 Video

Extra Lectures (Non-examinable)

  1. Lecture 38 - Hyperreal Numbers Video
  2. Lecture 39 - Predicate Logic: Ultraproduct of Structures and Los's Theorem Video
  3. Lecture 40 - Predicate Logic: Compactness Theorem Video
  4. Lecture Tutorial : Week 12 Video

Live Session

  1. Live Session 21-02-2024 Video
  2. Live Session 23-03-2024 Video
  3. Live Session 26-04-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Amit Kuber
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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