Set theory
4 points * First semester * Clayton * Prerequisites: MAP2011 or two of MAP2021, MAP2032, MAP2052
Objectives On the completion of this subject students will be able to understand Zermelo's theory of types; derive statements (informally) from the axioms; identify the different kinds of partial orderings; apply the rules for addition, multiplication and exponentiation of cardinal numbers, with or without the Axiom of Choice; understand the theory of ordinal numbers; simplify expressions involving ordinal addition, multiplication and exponentiation.
Synopsis Relations, functions (injective, surjective, bijective), operations, equivalences, cardinal numbers, cardinal arithmetic, order types, ordinal numbers. Axiom of choice, Zorn's Lemma, well order theorem. Zermelo-Fraenkel axioms.
Assessment Examinations (1.5 hours): 70% * Assignments: 30%
Prescribed texts
Lipschutz S Set theory and related topics Schaum, 1964
Recommended texts
Enderton H B Elements of set theory Academic Press, 1977
Halmos P R Naive set theory Van Nostrand, 1960
Kamke F Theory of sets Dover, 1950
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