Advanced Topics in Mathematical Logic: Forcing (V5A6)
Lecturer
- Dr. Philipp Lücke
- Dr. Philipp Schlicht
Time and place
- Lecture: Tuesday 14.15-16.00 in room 1.007 and Wednesday 10.15-12.00 in room 0.007.
Contents
The method of forcing was introduced by Paul Cohen in his proof of the independence of the Continuum Hypothesis and the Axiom of Choice. Forcing proved to be a remarkably general technique for producing a large number of models and consistency results. In this lecture, we present several important forcing constructions, in particular
- The consistency of PFA.
- Solovay's model of ZF+DC+"all sets of reals are Lebesgue-measurable" (Introduction, Intermediate models of forcing extensions, The Levy Collapse, Borel Codes, The proof of Solovay's theorem).
- Singularizing cardinals by forcing: Prikry forcing, Namba forcing and variations.
- Indestructibility of large cardinals.
- Failures of the Singular Cardinal Hypothesis from a supercompact cardinal.
- Precipitous and saturated ideals.
- The nonstationary ideal.
- Adding large cardinals by forcing (Generic square sequences, Threading square sequences by forcing).
- Stationary reflection (Introduction, Club shooting, Proof of the Harrington-Shelah reflection result, Simultaneous reflection).
- The tree property at successor cardinals.
The exams are on Friday, July 11 and Friday, August 01. The second exam is on Thursday, September 11.