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. 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 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 Lecture series Lecture 1 Propositional Logic Lecture 2 not available yet Assignments not available yet Examinations not available yet Recommended student evaluation scheme not available yet