Inner Model Theory Seminar

(SoSe 2023)

(SoSe 2023)

This is an introductory learning seminar for inner model theory. We will go through Farah's paper „The Extender Algebra and Sigma^2_1-absoluteness“. After recalling some notions from last semester such as extenders, Woodin cardinals and iterations trees (which allows people not attending the previous seminar to follow), we introduce Woodin's extender algebra and prove its basic properties. Then we consider applications to generic absoluteness and the existence of divergent models of AD+.

The seminar takes place

**Wednesdays 12:30 - 14:00**in the Dissertantenraum (TU Wien Freihaus, green area, 8th floor).

After successful completion of the course, students and other participants are able to follow basic inner model theoretic literature. They will master linear iterations of ultrapowers and extenders as well as the basics of iteration trees and applications. This seminar is an ideal preparation for a follow-up seminar taking place in the summer semester.

The inner model theory seminar will be a weekly seminar with alternating speakers, including students, guests, and members of the research unit. Giving a talk and active participation are mandatory to successfully complete the course. The speaker is responsible for preparing the talk and selecting highlights from the material. The lecturer will offer help in the preparation of the talk, both for scientific questions and didactic issues.

### Lectures

**Mar 01, 2023**, Sandra Müller: Organisational meeting, overview and introduction**Mar 08, 2023**, Nick Chapman: Infinitary propositional logic (§1 in Farah's paper)**Mar 15, 2023**, Corey Switzer: Extenders, Woodin cardinals (§2 in Farah's paper)**Mar 29, 2023**, Lukas Schembecker: The extender algebra (§3 in Farah's paper)**Apr 19, 2023**, Fernando Barrera: Iteration trees, the iteration game (§3.1, 3.2 in Farah's paper)**Apr 26, 2023**, Lena Wallner: Genericity iterations (§4 in Farah's paper)**May 10, 2023**, Bartosz Wcislo: Genericity iterations for subsets of omega_1 (§4.1 in Farah's paper)**May 17, 2023**, Lukas Koschat: Absoluteness in L(R) (§5, 5.1 in Farah's paper)**May 24, 2023**, Lukas Koschat: Absoluteness for H(aleph_2) (§5.2 in Farah's paper)**Jun 14, 2023**, Takehiko Gappo: Universally Baire sets and absoluteness (§6.1 in Farah's paper)**Jun 21, 2023**, Takehiko Gappo: An iterable model with a Woodin limit of Woodin cardinals and divergent models of AD+ (§6, 6.2, 6.3 in Farah's paper)