21-702 Set Theory II

12 units, Carnegie Mellon University

This course is a sequel to 21-602 Set Theory. The main goal is to prove Solovay's theorem that Con(ZFC + an inaccessible cardinal) implies Con(ZF + DC + every set of reals is Lebesgue measurable). Topics covered include absoluteness theorems, Borel codes, the Levy collapse, product forcing, relative constructibility, and the basics of iterated forcing up to the consistency of Martin's Axiom. (Three 50 minute lectures)

Prerequisites: (21-355 (min B) or 21-235 (min B) or 21-455 (min B)) and (21-373 (min B) or 21-237 (min B)) and 21-602 (min B)

Offered: Spring 2026

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