# Logic Seminar

The Logic seminar is held on Wednesdays, usually at 12-14. During the spring 2023 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 2023

Wed 18.1.2023 12-14, C124

Vadim Weinstein: BLURRY FILTERS AND CLASSIFICATION BY COUNTABLE STRUCTURES (PART II: PROOFS)

(Joint work with Martina Lannella)

Abstract: This is a continuation of the talk given on Nov 9^{th} 2022. In the first talk we gave an overview of the field, main ideas, and results. In this, second, talk we dive into the details of the central proofs. The same abstract as for the first talk follows:

The Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras. The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this talk we introduce a weaker concept which we call the “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration from totally disconnected ones to a larger class. As an application of this method, we show that the following are completely classifiable by countable structures: the homeomorphism on 3-manifolds (also applicable to 2-manifolds; but this was known since 1971), and wild embeddings of Cantor sets in R³. By "classification" in this talk we mean classical Borel-reducibility.

Wed 25.1.2023 12-14, C124 (and zoom)

Jonathan Kirby: Around Zilber's quasiminimality conjecture

Abstract: About 25 years ago, Zilber conjectured that the complex field with the exponential function is quasiminimal: every definable subset is countable or co-countable. This conjecture has sparked a lot of activity over that time. For example, Zilber's part of the Zilber-Pink conjecture and the related work on functional transcendence came out of his early work towards the quasiminimality conjecture. Recently there has been significant progress towards proving the conjecture itself.

I will survey some of the work around the conjecture, including the nature of quasiminimality and its relationship to infinitary and classical first-order logic, and the recent result of Gallinaro and myself that the complex field equipped with complex power functions is quasiminimal.

Wed 1.2.2023 12-14, Zoom

Christian** **d'Elbée: Fields with a generic multiplicative endomorphism

Abstract: The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I will mention some features that appear in ACFH, notably a conjecturally suboptimal description of Shelah's forking and the ubiquity of definable groups whiches theories are pseudofinite-cyclic, that is, elementary equivalent to an ultraproduct of finite cyclic groups.

Wed 8.2.2023 12-14, C124

William Mance: Descriptive complexity in number theory and dynamics

Abstract: Informally, a real number is normal in base $b$ if in its $b$-ary expansion, all digits and blocks of digits occur as often as one would expect them to, uniformly at random. Kechris asked several questions involving descriptive complexity of sets of normal numbers. The first of these was resolved in 1994 when Ki and Linton proved that the set of numbers normal in base $b$ is $\Pi_3^0$-complete. Further questions were resolved by Becher and Slaman. Many of the techniques used in these proofs can be used elsewhere. We will discuss recent results where similar techniques were applied to solve a problem of Sharkovsky and Sivak and a question of Kolyada, Misiurewicz, and Snoha. Furthermore, we will discuss a recent result where the set of numbers that are continued fraction normal, but not normal in any base $b$, was shown to be complete at the expected level of $D_2(\Pi_3^0)$. An immediate corollary is that this set is uncountable, a result (due to Vandehey) only known previously assuming the generalized Riemann hypothesis.

Wed 15.2.2023 12-14, C124

Yasir Mahmood: TBA

Wed 22.2.2023 12-14, C124

Max Sandström: TBA

Wed 1.3.2023 12-14, C124

TBA

Wed 8.3.2023 12-14, C124

Exam week

Wed 15.3.2023 12-14, C124

Åsa Hirvonen: TBA

Wed 22.3.2023 12-14, C124

TBA

Wed 29.3.2023 12-14, C124

Nicolás Nájar: TBA

Wed 5.4.2023 12-14, C124

TBA

Wed 12.4.2023 12-14, C124

Easter

Wed 19.4.2023 12-14, C124

TBA

Wed 26.4.2023 12-14, C124

TBA

Wed 3.5.2023 12-14, C124

TBA

Wed 10.5.2023 12-14, C124

Exam week