Introduction to Set Theory

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.

[edit] Course requirements

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

• knowledge of basic Pure Mathematics
• knowledge of formal proofs

[edit] Course outline

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

[edit] Lecture series

• Lecture 1 Propositional Logic
• Lecture 2 not available yet

[edit] Assignments

not available yet

[edit] Examinations

not available yet

[edit] Recommended student evaluation scheme

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