Introduction to Set Theory

Introduction to Set Theory


This course aims to provide a thorough introduction to the subject of set theory. We will cover the following: Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences.

Course requirements

edit

The following knowledge is required or desirable on commencement of study of this course:

Course outline

edit

This is an approximate depiction of the course:

  • Propositional Logic
  • Axiomatic Approach
  • Unions and Intersections
  • Algebra of Sets
  • Ordered Pairs
  • Relations
  • Functions
  • Ordering Relations
  • Cardinal Arithmetic
  • Partial, Linear Orderings
  • Well Orderings
  • Comparison Theorem for Well Orderings
  • Isomorphisms
  • Transfinite Recursion Theorem
  • Replacement Axioms
  • Epsilon-Images
  • Ordinals
  • Ordinal Numbers
  • Ordinal Arithmetic

Lecture series

edit

Assignments

edit

not available yet

Examinations

edit

not available yet

edit

not available yet