Math 2.0

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Set Theory and Mathematical Logic M7H8NFY4WH

URIm2://res/M7H8NFY4WH
Kindcourse
CreatorsAmit Kuber (instructor)
Date2024-01-19
MSC03-XX
Scopein
Idscourse 05pjsgx75:111104416

Expressions

e1: edition

Languageen
Date2024-01-19
Contents
  • part 1: week-01
  • session 1: Lecture 01: Introduction to Set Theory
  • session 2: Lecture 02: Operations on Sets, and Functions
  • session 3: Lecture 03: Bijective Functions
  • part 2: week-02
  • session 4: Lecture 04: Equivalence Relations and Partitions
  • session 5: Lecture 05: Cantor-Schroder-Bernstein Theorem
  • session 6: Lecture 06: Natural Numbers in ZF Set Theory
  • part 3: week-03
  • session 7: Lecture 07: Standard number systems in ZF set theory
  • session 8: Lecture 08: (Finitary) power sets and countability
  • session 9: Lecture 09: Bijections of the set of real numbers: Dedekind cut and Cantor’s middle-third set
  • session 10: Lecture 10: Bijections of the set of real numbers: Continued Fractions
  • part 4: week-04
  • session 11: Lecture 11 - Principles of Mathematical Induction
  • session 12: Lecture 12 - Ordinal Numbers
  • session 13: Lecture 13 - Ordinal Arithmetic
  • session 14: Lecture 14 - Cardinal Numbers and Cardinal Arithmetic
  • session 15: Lecture Tutorial - Week 4
  • part 5: week-05
  • session 16: Lecture 15 - Partial Orders
  • session 17: Lecture 16 - Lattices
  • session 18: Lec 17 - Equivalents of the Axiom of Choice (AC): Zorn's Lemma (ZL) and Well-ordering theorem (WOT)
  • session 19: Lecture Tutorial - Week 5
  • part 6: week-06
  • session 20: Lecture 18 - Boolean Algebras
  • session 21: Lecture 19 - Stone's Representation Theorems for Boolean Algebras
  • session 22: Lecture 20 - Some Exercises on Boolean Algebras
  • session 23: Lecture 21 - Ultrafilters in Boolean Algebras
  • part 7: week-07
  • session 24: Lecture 22 - Introduction to Mathematical Logic
  • session 25: Lecture 23 - Propositional Logic: Language, Formulas and Valuations
  • session 26: Lecture 24 - Propositional Logic: Logical Equivalence and Lindenbaum-Tarski Algebra
  • session 27: Tutorial : Week 07
  • part 8: week-08
  • session 28: Lecture 25 - Propositional Logic: Normal Forms of Formulas and Adequacy of Connectives
  • session 29: Lecture 26 - Propositional Logic: Semantic Consequence Relation
  • session 30: Lecture 27 - Propositional Logic: Syntactic Consequence Relation
  • session 31: Lecture 28 - Deduction Theorem (Continued...)
  • session 32: Lecture Tutorial : Week 08
  • part 9: week-09
  • session 33: Lecture 29 - Propositional Logic: Consistency and Soundness Theorem
  • session 34: Lecture 30 - Propositional Logic: Completeness Theorem - Part I
  • session 35: Lecture 31 - Propositional Logic: Completeness Theorem - Part II
  • session 36: Lecture 32 - Compactness Theorem and Konig's Lemma
  • session 37: Lecture Tutorial : Week 09
  • part 10: week-10
  • session 38: Lecture 33 - Introduction to First-Order Predicate Logic
  • session 39: Lecture 34 - Predicate Logic: Terms and Formulas
  • session 40: Lecture 35 - Predicate Logic: Validity of Formulas
  • session 41: Lecture Tutorial : Week 10
  • part 11: week-11
  • session 42: Lecture 36 - Predicate Logic Substructures, Semantic Consequence Relation, and Models of Theories
  • session 43: Lecture 37 - Predicate Logic: Standard Logical Equivalences, Normal Forms, and Definable Sets
  • session 44: Lecture Tutorial : Week 11
  • part 12: Extra Lectures (Non-examinable)
  • session 45: Lecture 38 - Hyperreal Numbers
  • session 46: Lecture 39 - Predicate Logic: Ultraproduct of Structures and Los's Theorem
  • session 47: Lecture 40 - Predicate Logic: Compactness Theorem
  • session 48: Lecture Tutorial : Week 12
  • part 13: Live Session
  • session 49: Live Session 21-02-2024
  • session 50: Live Session 23-03-2024
  • session 51: Live Session 26-04-2025

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