Seminar
Logic Seminar
The Logic seminar is held on Wednesdays, usually at 12-14. During the spring 2025 we will have both on-site and online talks, and we try to keep the page updated on when we have which kind.
The permanent Zoom room for the seminar is: https://helsinki.zoom.us/j/62891400777?pwd=UldCeThTaTJVQjUzUFo4S2ErcndNQT09 (Meeting ID: 628 9140 0777, Passcode: 164195)
PLEASE NOTE: Due to the prevalence of zoom talks given by scholars based in various time zones, the times that the seminar meets will occasionally change from the usual 12-14 slot. Also, if not separately specified, the talks always start at a quarter past.
The seminar is led by prof. Juha Kontinen and Ulla Karhumäki.
Schedule of the spring term 2025
Wed 15.01.2025 12 -14, C124
No seminar
Wed 22.01.2025 12 -14, C124
Jouko Väänänen: The extended logic paradigm in inner model theory
Abstract: I consider inner models arising from extended logics, as in my joint paper with Kennedy and Magidor and in my previous talk 9.10.2024. I introduce a new inner model of this kind, denoted C2(omega), based on the second order logic in which second order variables
range over countable subsets of the domain. I give some results about large cardinals in C2(omega) and also about its relationship with C(aa). I also discuss the inner model HOD1 arising from existential second order logic. This is joint work with Menachem Magidor.
Wed 29.01.2025 12 -14, C124
Reijo Jaakkola: Expressing boundedness in static computational logic
Abstract: Static computational logic (SCL), which is an extension of first-order logic via recursion, was studied extensively in [1]. In particular, a semantical variant of SCL, called bounded SCL, was introduced. This logic can naturally express properties related to boundedness, such as "the diameter of a graph is finite" or "there is a uniform finite bound on lengths of descending chains in a given linear order". In [1] it was left open whether bounded SCL is contained in SCL. The main purpose of this talk is to present a proof showing that this containment indeed holds. Additionally, I will highlight connections between SCL and other frameworks for recursion discussed in the literature.
Wed 05.02.2025 12 -14, C124
No seminar
Wed 12.02.2025 12 -14, C124
Menachem Magidor: On generic absoluteness of \Sigma_2^2 statements about the reals
Abstract: Generic absoluteness for a class of Set Theoretic statements is the fact that the truth of any statement in the class can not be changed by forcing. There is Mathematical and Philosophical interest in showing that extensive classes of statements are forcing absolute. Interesting phenomena is that for some classes of statements are not forcing absolute over any model of set theory but they become forcing absolute if one assumes the existence of a certain kind of large cardinals.
One can also consider forcing absoluteness of a certain class of sentences conditional on a given statement Φ. Namely that truth of sentences in the class can not be changed by forcing, provided both the ground model and the generic extension satisfy the sentence Φ. A typical example is the theorem by Woodin that every statement about L(R) is forcing absolute if one assumes the existence of a proper class of Woodin cardinals. Another theorem is that \Sigma_1^2 statements about the reals are forcing absolute conditioned on the Continuum Hypothesis, provided one assume the consistency of a proper class of measurable Woodin cardinals.
Several authors conjectured that \Sigma_2^2 statements are forcing absolute conditioned on the combinatorial principle \diamond_{ω_1} , provided one assumes the existence of a proper class of the right notion of large cardinals. The truth of this conjecture will have a far reaching consequences for the inner models program.
In the talk we shall survey some arguments for showing forcing absoluteness of certain classes and give a scenario for proving the conjecture about \Sigma_2^2 statements, conditioned on \diamond_{ω_1} .
Wed 19.02.2025 12 -14, C124
No seminar
Wed 26.02.2025 12 -14, C124
Andres Villaveces: Compressing Information as a dividing line in model theory
Abstract: I will describe first from a rather general perspective some connections between the notion of a NIP (also called "dependent") first order theory, due to Shelah, and various notions arising from learning theory around the problem of compressibility of information. I will then address current work in the problem of generalizing the notion of a NIP first order theory to the more general context of AECs (I will describe three approaches: one due to myself, with Grossberg and Vandieren, another due to Wentao Yang, and finally another one in our current work with Nicolás Nájar and Saharon Shelah.)
Wed 05.03.2025, Exam week (no seminar)
Wed 12.03.2025 12 -14, C124
Nadja Hempel: Groups and Fields in higher classification theory
Abstract: A key goal in model theory is distinguishing between tame structures (e.g. the complex field) and wild structures (e.g. the ring of integers). This distinction was introduced by Shelah in the 1970s (Shelah’s Classification Theory) and is based on restricting combinatorial pattern given by definable binary relations. At the apex are the stable theories, such as the complex field, with two complementary extensions: NIP theories (including p-adic fields) and simple theories (such as pseudofinite fields). In this talk, we briefly discuss fields whose theory is tame in the above sense. Afterwards, we leave the binary world, and introduce “n-ary” Classification theory. Instead of “controlling” 2-ary relation, we only assume that n-ary relations are tame. We give examples and discuss groups and fields within these classes of theories.
Wed 19.03.2025 12 -14, C124
Melissa Antonelli: TBA
Wed 26.03.2025 12 -14, C124
Rosario Mennuni: TBA
Wed 02.04.2025 12 -14, C124
TBA
Wed 09.04.2025, 12-14, C124
TBA
Wed 16.04.2025, 12-14, C124
TBA
Wed 23.04.2025, Easter break (no seminar)
Wed 30.04.2025 12 -14, C124
TBA
Talks of the spring term 2023
Talks of the fall term 2022
Talks of the spring term 2022
Talks of the fall term 2021
Talks of the spring term 2021
Talks of the fall term 2020
Talks of the spring term 2020
Talks of the fall term 2019
Talks of the spring term 2019
Talks of the fall term 2018Seminar talks fall 2018
Talks of the spring term 2018Seminar talks spring 2018
Talks of the fall term 2017Seminar talks fall 2017
Talks of the spring term 2017Seminar talks spring 2017
Talks of the fall term 2016Seminar talks fall 2016
Talks of the spring term 2016Seminar talks spring 2016
Talks of the fall term 2015Seminar talks fall 2015
Talks of the spring term 2015Seminar talks spring 2015
Talks of the fall term 2014Seminar talks fall 2014
Talks of the spring term 2014Seminar talks spring 2014
Talks of the fall term 2013Seminar talks fall 2013
Talks of the spring term 2013Seminar talks spring 2013
Talks of the fall term 2012Seminar talks fall 2012
Older talks (2011-2012)