#### Talks during the spring term 2021

Wednesday 20.1.2021 12-14

Jouko Väänänen: Three fundamental games in logic (Slides, Video recording)

Wednesday 27.1.2021 12-14~~Gianluca Grilletti: TBA~~ **cancelled**

Wednesday 3.2.2021 12-14

Grigor Sargsyan: Forcing failures of square at omega_3 over models of determinacy, and the convergence of Kc constructions.

Abstract: We will present recent results showing that contrary to widely held beliefs that the failure of square_{omega_3} and

square(omega_3) along with 2^omega_2=omega_3 is weaker than a Woodin cardinal that is a limit of Woodin cardinals. This rules out

one of the classic approaches to the inner model problem via K^c constructions.

Wednesday 10.2.2021 12-14

Fan Yang: Propositional union closed team logics

Wednesday 17.2.2021 16-18 **NOTE THE TIME CHANGE**

Toby Meadows: Risk and Theoretical Equivalence in Foundations of Mathematics

**Abstract: **I will outline a way of understanding the content of theories which is intended to be invariant upon the language in which we articulate them. To motivate this, I'll use some simple probability principles as a guide. The resultant system exploits model-to-model rather than theory-to-theory relations. I'll then show that the generic multiverse can be seen as an example of this kind framework in practice.

Wednesday 24.2.2021 12-14

Colin Rittberg: The Virtues and Vices in Mathematics project

Abstract: In this talk I present the motivations, methodology, and aspirations of the VaViM project; https://vavimproject.wixsite.com/home. The project philosophically studies injustices in the knowledge-making processes of mathematics.

Wednesday 3.3.2021 12-14

Grigor Sargsyan: The exact strength of Sealing

Abstract: Sealing is a generic absoluteness statement which was introduced by Woodin. First given a generic object g, let Gamma^infty_g be the set of universally Baire sets of V[g] and R_g be the set of reals of V[g].

Sealing (essentially) says for all V-generic g and all V[g]-generic h there is an embedding

j: L(Gamma^infty_g, R_g)-> L(Gamma^infty_g*h, R_g*h)

Thus, in a way, Sealing says that there cannot be independence results about universally Baire sets, and as such it is a generalization of Shoenfield's absoluteness theorem.

It is an open problem if large cardinal imply Sealing. No canonical inner model can satisfy it, and so if some large cardinal implies it then its inner model theory has to be significantly different than the modern norms. Surprisingly, Woodin showed that if there are proper class of Woodin cardinals and delta is supercompact then collapsing 2^{2^delta} to be countable forces Sealing. Because of its impact on the inner model problem and because of Woodin's result, it seemed that Sealing must be as strong as supercompacts. However, the speaker and Nam Trang showed that it is weaker than a Woodin cardinal that is a limit of Woodin cardinals. We will exposit this theorem and will also explain its consequences on the inner model problem.

Wednesday 10.3.2021 12-14

Exam week, no seminar

Wednesday 17.3.2021 12-14

Aleksi Anttila: Axiomatizing a logic for Free Choice

I present axiomatizations and discuss the expressive power of several modal team logics. One of these is an extension of Maria Aloni's Bilateral State-Based Modal Logic, which can be used to account for Free Choice inferences and other linguistic phenomena.

Wednesday 24.3.2021 12-14

Françoise Point: Topological large fields of characteristic zero with a generic derivation.

Model theory of differential topological fields of characteristic zero is traditionally divided in two main directions, whether one assumes a compatibility between the derivative and the topology.

We illustrate the first direction with recent results of Aschenbrenner, van den Dries et van der Hoeven on the (ordered) field of transseries.

Then we concentrate on the case where the derivative has a generic behaviour, putting a largeness hypothesis on the field. We introduce what we called L-open theories T of topological fields (of characteristic zero). We describe some transfer results from the model theoretic properties of T to the class of existentially closed differential expansions of T. We will also explain a connection with some recent work of W. Johnson on fields of dp-finite rank.

We show how this particular framework can be applied to dense pairs of models of T. Finally we associate to a definable group in such differential expansion an L-definable object, using the group configuration as stated by K. Peterzil for o-minimal theories.

This is mostly joint work with Pablo Cubidès.

Wednesday 31.3.2021 12-14

Tjeerd Fokkens: On the Reduction of Quantum Teams (Slides)

Abstract: Bell inequalities are mathematical expressions that intend to describe a certain quantum physics experiment. They can be derived under classical assumptions. These inequalities can, however, be violated in practice. Casting them into a logical mould might shine more light on the underlying mechanism of contextuality. Using Quantum Team Logic (QTL) and its quantum team semantics, an algorithm is described that can be used to demonstrate contextuality. Moreover, an open problem is partly solved regarding the axiomatization in QTL of the quantum analogue of Bell inequalities, making use of Tsirelson’s bound.

Wednesday 7.4.2021 12-14

Easter break, no seminar

Wednesday 14.4.2021 12-14

Joni Puljujärvi: Team Semantics and Independence Notions in Quantum Physics

Wednesday 21.4.2021 12-14

John Lång: The model D_{∞}

Abstract: Lambda-terms in pure untyped lambda-calculus are often characterised as anonymous functions. Formalising this simple description is less trivial than it seems. As a general term formation rule, juxtaposing any two lambda-terms yields a new lambda-term called an application. If the left-hand side term can be interpreted as a function f and the right-hand side term can be interpreted as an element x in the domain of f, then the application can be interpreted as the value f(x). This naïve interpretation breaks down when a lambda term is applied to itself. On one hand, self-application enables unrestricted recursion, making lambda-calculus Turing-complete. On the other hand, combining self-application and logical connectives may also lead into paradoxes and contradictions. In the late 1960'ies, Dana Scott found a way to represent pure untyped lambda-calculus in set theory in a logically sound way in what he calls the first "mathematical" model of lambda-calculus, the model D∞. This model is a combination of order theory, topology, and categorical thinking that started the fields of denotational semantics and domain theory.

Wednesday 28.4.2021 12-14

Dag Westerståhl : Completeness versus (Carnap) categoricity

Abstract: I will make some easy observations and raise some issues concerning the following c’s (in alphabetic order): Carnap, categoricity, completeness, compositionality, consequence, constants, and context. What is the point of completeness (of a logic)? Is the so-called abstract completeness theorem just an aspect of Tarski’s notion of consequence? What is the role of compositionality in this setting? How do we single out the (logical) constants? What to do about Carnap’s problem --- the underdetermination of the meaning of logical constants by the corresponding consequence relation? Which generalized quantifiers are logical? Does completeness matter to logicality? These are no doubt deep and difficult questions, but I’m hoping some simple remarks can still be helpful.

Wednesday 5.5.2021 12-14

Davide Quadrellaro: Algebraisability and Algebraic Completeness of Intermediate Inquisitive and Dependence Logics

Wednesday 12.5.2021 12-14

Exam week, no seminar

Wednesday 19.5.2021 12-14

Katrin Tent: Simple automorphism groups

The automorphism groups of many homogeneous structures (Riemannian symmetric spaces, projective spaces, trees, algebraically closed fields, Urysohn space etc) are abstractly simple groups - or at least are simple after taking an obvious quotient.

We present criteria to prove simplicity for a broad range of structures based on the notion of stationary independence.

Wednesday 26.5.2021 12-14

Vadim Kulikov: Various embeddability relations on linear and circular orders with connections to knot theory (joint work with: Martina Iannella, Alberto Marcone and Luca Motto Ros)

Abstract: It is known that the isomorphism of linear orders can be Borel-reduced to the equivalence of wild knots by arranging singularities on the knot in the order type of a given linear order. By looking instead at the sub-arc relation, one is naturally drawn to consider convex embeddability of linear orders. A linear L order is convex-embeddable into L', if L is isomorphic to a convex subset of L'. More generally one can define quasiorders on the class of linear orders by saying that L is "embeddable" to L', if L can be partitioned in "some nice way" into convex subsets each of which can then be convexly embedded to L' so that the ordering of these parts is also preserved. Motivated partially by knots, partially by elegance and curiosity, we also consider such relations on circular orders. We prove a range of Borel- and Baire-reducibility results on these quasiorders and the related equivalence relations of bi-embeddability.