The Baltic Set Theory Seminar

Topics:

1. (September-October) Grigor Sargsyan, A course on large cardinals
   
2. (November-December) Tutorials by the Leaders of the Set Theory portion of Structures Semester
   
3. Below is the list of the Tutorial Speakers. Please note that the tutorials will take place at the Gdansk branch of IMPAN.
   
4. Omer Ben Neria (Hebrew University)
   Ralf Schindler (University of Münster)
   Matteo Viale (University of Turin)
   John Steel (UC Berkeley)
   Boban Velickovic (Paris)
   Jouko Väänänen
   Jindra Zapletal
   
5. The infor for Tutorials is listed below.

Time: 15:00-16:30, Warsaw/Paris Time.

Zoom Info:

Meeting ID: 897 1539 0286

Passcode: 763015

Abstract: The minicourse will outline the methodology of obtaining independence results in the choiceless theory ZF+DC, as described in the book Geometric Set Theory with coauthor Paul Larson. Within its scope, the method is much more efficient and intuitive than all earlier ones. It allows detailed ZF+DC comparison of various objects currently considered in Borel context.

Lecture 1 Info
Date: November 20, 2023
Time: 13:30-14:30
Place: IMPAN Warsaw, Room 405
Abstract: I will sketch the main concerns, definitions, and general theorems. As one consequence of this development, I will get the following: It is consistent with ZF+DC that there is a non-principal ultrafilter on natural numbers, yet no maximal almost disjoint family of sets of natural numbers exists.

Lecture 2 Info
Date: November 21, 2023
Time: 13:30-14:30
Place: IMPAN Warsaw, Room 405
Abstract: I will show how to stratify the amalgamation arguments used in geometric set theory. I will apply the stratification to independence problems in algebraic geometry: It is consistent with ZF+DC to have a Hamel basis for R but not a transcendence basis for R over Q. For any positive integer n, let Gn be the graph on n-dimensional Euclidean space connecting points of rational Euclidean distance. It is consistent with ZF+DC that Gn has countable chromatic number while Gn+1 does not.

Lecture 3 Info
Date: November 22, 2023
Time: 13:30-14:30
Place: IMPAN Warsaw, Room 405
Abstract: I will show how to obtain independence results in the realm of locally countable descriptive combinatorics. A sample theorem: Let G be a locally finite Borel graph of true chromatic number n. It is consistent with ZF+DC that G has chromatic number at most 2n-1, and there is no Vitali set.

Abstract: Inspired by P_max, we define and explore the *-versions of various forms of Martin’s Maximum. While the *-version of BMM is equivalent to BMM (by a result of Asperó and the speaker), the *-version of full MM might be strictly stronger than MM and in fact the former isn’t even known to be consistent. The new result will be the construction of a ZFC-model of the *-version of MM for antichains of size \aleph_2. Doing the same for \aleph_3 is a problem that is wide open and leads to interesting set theoretical questions which are currently explored by several people.

Tutorial 1
Date: November 2nd, 2023
Time: 16:45-17:45
Place: University of Gdansk, Department of Mathematics, Room D003
Crosslisted as Gdansk Logic Colloquim

Tutorial 2
Date: November 3rd, 2023
Time: 14-15
Place: Mariacka 34/36

Tutorial 3
Date: November 6, 2023
Time: 14-15
Place: Mariacka 34/36

Tutorial 1
Date: November 2nd, 2023
Time: 15:30-16:30
Place: University of Gdansk, Department of Mathematics, Room D003
Crosslisted as Gdansk Logic Colloquim

Tutorial 2
Date: November 9th, 2023
Time: 11-12
Place: Mariacka 34/36

Tutorial 3
Date: November 10th, 2023
Time: 11-12
Place: Mariacka 34/36

Two additional lectures:

Date: November 15, 2023
Time: 14:15-15:15
Title: Higher derived limits
Place: IMPAN, Warsaw
Crosslisted as IMPAN Colloquium

Date: November 17, 2023
Time: 12-13
Title:
Place: IMPAN, Warsaw
Crosslisted as a talk in Perspectives on Set Theory

Tutorial 1
Date: October 23, 2023
Time: 12-13
Place: Mariacka 34/36

Tutorial 2
Date: October 24, 2023
Time: 12-13
Place: Mariacka 34/36

Tutorial 3
Date: October 26, 2023
Time: 17-18
Place: University of Gdansk, Department of Mathematics, Room D003
Crosslisted as Gdansk Logic Colloquim

Topics:

1. Matteo Viale, Generic absoluteness theorem for the $\omega_1$ Chang model conditioned to $MM^{+++}$.
   
2. Paul Larson, A course on $AD^+$.

Topics:

1. Sandra Mueller, Stationary-Tower-Free Proof of Woodin’s Sealing Theorem. </td></tr>
2. Matteo Viale, Generic absoluteness theorem for the $\omega_1$ Chang model conditioned to $MM^{+++}$.
   
3. Notes from Sandra’s talk.
   

Topics:

1. Finish the proof of Neeman’s Handbook Article, Determinacy in L(R).
   
2. Learn a new Stationary-Tower-Free Proof of Woodin’s Sealing Theorem, which lifts the well-known absoluteness theorems for L(R) to the collection of the universally Baire sets.
   
3. Learn about virtual models.