Advanced Topics in Mathematical Logic: Forcing and large cardinals (V5A7)
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 1.007.
Lecture notes
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 using large cardinals. The lecture continues last semester's "Models of Set Theory II" course.
Schedule
- April 12 - Philipp Schlicht - Normal ultrafilters on Pκ(λ)
- April 13 - Philipp Schlicht - Supercompact cardinals
- April 19 - Philipp Schlicht - Characterizations of supercompact cardinals
- April 20 - Philipp Schlicht - Some lemmas on forcing and names
- April 26 - Philipp Schlicht - The proper forcing axiom
- April 27 - Philipp Schlicht - Consistency of the proper forcing axiom
- May 03 - Philipp Schlicht - Axiom A forcings
- May 04 - Philipp Schlicht - A forcing axiom for Axiom A forcings
- May 10 - Philipp Lücke - The Open Colouring Axiom
- May 11 - Philipp Lücke - The Open Colouring Axiom
- May 17 - no lecture
- May 18 - no lecture
- May 24 - Philipp Lücke - Consequences of PFA: The size of the continuum
- May 25 - no lecture
- May 31 - Philipp Lücke - Consequences of PFA: The size of the continuum
- June 01 - Philipp Lücke - Consequences of PFA: The tree property
- June 07 - Philipp Lücke - Consequences of PFA: The tree property
- June 08 - Philipp Lücke - Consequences of PFA: Weak Kurepa trees
- June 14 - Philipp Lücke - Consequences of PFA: Weak Kurepa trees
- June 15 - Philipp Lücke - Consequences of PFA: The failure of square
- June 21 - Philipp Lücke - Consequences of PFA: The failure of square
- June 22 - Philipp Schlicht - Forcing with sequences of models
- June 28 - Philipp Schlicht - Forcing with sequences of models
- June 29 - Philipp Schlicht - Forcing with sequences of models
- July 05 - Philipp Schlicht - Forcing with sequences of models: Strong properness
- July 06 - Philipp Schlicht - Forcing with sequences of models: The tree property
- July 12 - Philipp Schlicht - Forcing with sequences of models: PFA
- July 13 - Philipp Schlicht - Forcing with sequences of models: PFA