Introduction to Set Theory

< Wikiversity < Wikiversity:School of Mathematics < School:Mathematics/Undergraduate/Pure Mathematics

## Introduction to Set Theory

### An introductory course from the School of Mathematics

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

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

* knowledge of basic Pure Mathematics
* knowledge of formal proofs

## Course outline

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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

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* Lecture 1 Propositional Logic
* Lecture 2 not available yet

## Assignments

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not available yet

## Examinations

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not available yet

## Recommended student evaluation scheme

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not available yet