Singapore talks

At the NUS summer school in logic, I'm going to give a lecture course on Forcing axioms and Pmax.

In 2019, in joint work with with D. Aspero we proved that the ++ version of Martin's Maximum implies Woodin's Pmax axiom (*). This amalgamated two maximality principles which decide the size of the continuum and which prior to our result had sometimes been seen as competitors. Our result in fact produces a specific version of the \Omega conjecture, and it sheds light on the duality of forcing over ZFC models with large cardinals and forcing over determinacy models. I will give an introduction to forcing axioms as well as the (*) principle and give a complete proof of my result with Aspero. I will produce further applications of our method and discuss the extent to which we might be able to show that consistent statements may be forced over V. After having shown further results on variants and extensions of (*), I will discuss open questions for future research.

As nonmandatory background reading, the content of which is to be partially discussed during my talks, I recommend:
  1. Notes produced by Jiaming Zhang on a course I gave at Fudan University: 1st talk, 2nd talk, 3rd talk, 4th talk, 5th talk.
  2. Notes on a talk at Wuhan University.
  3. K. Kunen, Set theory. An introduction to independence proofs, Elsevier 1980, Chapters I, II, VII, and VIII.
  4. R. Schindler, Set theory. Exploring independence and truth, Springer 2014, Sections 6.1, 6.2, 7.1, 8.1, 10.3, 12.1.
  5. T. Jech, Set theory. The third millenium edition, Springer 2003, Chapter 37.
  6. P. Larson, Forcing over models of determinacy, in: Handbook of Set Theory (Foreman, Kanamori, eds.) vol. 3, Springer 2010, p.2121-2177.
Tentative schedule:

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