Bob Alan Dumas
Development of axiomatic set theory up to and including the consistency of the Axiom of Choice and Continuum Hypothesis with the Zermelo-Fraenkel Axioms.
We will begin the course with a brief treatment of the axioms of Zermelo-Fraenkel set theory (ZF), ordinal numbers, and cardinality. We will define the axiom of choice (AC) and prove the numerous useful equivalences in ZF. We will also cover elementary cardinal arithmetic, the continuum hypothesis, and the generalized continuum hypothesis. We will define the axiom of constructibility (V=L), and show that if ZF is consistent then ZF + V=L is consistent. We then show that AC and CH hold in ZF + V=L, hence ZFC + CH is consistent, provided that ZF is consistent. TEXT: Set Theory, Jech.
Student learning goals
General method of instruction
Class assignments and grading