Set Theory II

12 units · Graduate

Intermittent: 12 units 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: ( 21-455 Min. grade B or 21-235 Min. grade B or 21-355 Min. grade B) and ( 21-237 Min. grade B or 21-373 Min. grade B) and 21-602 Min. grade B