Inner Model Theory Seminar

(WiSe 2022)

(WiSe 2022)

This is an introductory learning seminar for inner model theory. We will go through Steel's Lectures "An Introduction to Iterated Ultrapowers" and introduce measures, embeddings, iterated ultrapowers, comparison, extenders, linear iterations via extenders, iteration trees of length omega, and iteration trees of transfinite length. Afterwards, we consider applications, including Woodin's extender algebra.

The seminar takes place

**Thursdays 13:00 - 14:30**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

**Oct 06, 2022**, Sandra Müller and Julia Millhouse: Introduction, ultrafilters, ultrapowers**Oct 13, 2022**, Martin Goldstern: Well-founded ultrapowers (Lecture 1 in Steel's notes starting from Lemma 1.2)**Oct 20, 2022**, Lukas Koschat: Iterated ultrapowers (Lecture 2 in Steel's notes)**Oct 27, 2022**, Benjamin Siskind: Applications of iterated ultrapowers (Lecture 2 in Steel's notes)**Nov 03, 2022**, Lukas Schembecker: Canonical inner models (Lecture 3 in Steel's notes up to Definition 3.4)**Nov 10, 2022**, Corey Switzer: Comparisons (Lecture 3 in Steel's notes starting from Definition 3.4)**Nov 17, 2022**, Rouholah Hoseini Naveh: Extenders (Lecture 4 in Steel's notes)**Nov 24, 2022**, Lena Wallner: Computing large cardinal strength (Lecture 4 in Steel's notes)**Dec 01, 2022**, Lukas Koschat: Linear iteration via extenders (Lecture 5 in Steel's notes)**Dec 15, 2022**, Takehiko Gappo: Iteration trees of length omega, part I (Lecture 6 in Steel's notes), for notes see here**Jan 12, 2023**, Takehiko Gappo: Iteration trees of length omega, part II (Lecture 6 in Steel's notes), for notes see here**Jan 19, 2023**, Takehiko Gappo: Iteration trees of length omega, part II (Lecture 6 in Steel's notes), for notes see here**Jan 26, 2023**, Rahman Mohammadpour: Iteration trees of transfinite length (Lecture 7 in Steel's notes)