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# Logic Seminar

The Logic seminar is held on Wednesdays at 12-14 in C124. After the seminar we have coffee together at 14-15 in the coffee room on the 4th floor.

The seminar is led by Doc. Tapani Hyttinen and university lecturer Juliette Kennedy.

#### Schedule of the spring term 2018

Wed 17.1.2018 12-14, C124
Yurii Khomskii: Projective maximal independent families

Wed 24.1.2018 12-14, C124
Fan Yang: Deriving and generalizing Arrow’s Theorem in dependence and independence logic

Wed 31.1.2018 12-14, C124
Fan Yang: Deriving and generalizing Arrow’s Theorem in dependence and independence logic, continued

Wed 7.2.2018 12-14, C124
Tim Gendron: Quasicrystals and the Quantum Modular Invariant

Abstract: Hilbert’s 12th problem asks for an explicit description of the Hilbert and ray class fields of a global field $K$. It was inspired by the Theorem of Weber-Fueter, where it is shown that the Hilbert class field of $K$ quadratic and complex over $\mathbb{Q}$ is generated by the modular invariant of any element of $K-\mathbb{Q}$. For $K=\mathbb{Q}(\theta )$ a real quadratic extension of $\mathbb{Q}$ we conjecture that the Hilbert class field is generated by a weighted product of the values of $j^{\rm qt}(\theta)$ where $j^{\rm qt}$ is a discontinuous and multi valued function called the quantum modular invariant. In the case of a real quadratic field of positive characteristic, this conjecture has been verified using the theory of Drinfeld-Hayes modules, wherein the values of $j^{\rm qt}$ are shown to be the modular in invariants of certain ideals in a “small” Dedekind ring. Recently Richard Pink has shown that the same is true in characteristic zero using a quasicrystalline analog of Dedekind ring. We show that the set of quasicrystalline ideals naturally form a Cantor set on which the modular invariant is continuous. We end by considering the new frontier of quasicrystalline algebraic number theory and its prospects for providing a basis for a Drinfeld-Hayes theory in characteristic zero that may eventually allow one to solve Hilbert’s 12th problem for real quadratic extensions of $\mathbb{Q}$.

Wed 14.2.2018 12-14, C124
Fan Yang: Questions and dependency in intuitionistic logic

Wed 21.2.2018 12-14, C124
Fausto Barbero: Interventionist counterfactuals in causal team semantics

Abstract: Teams and multiteams are adequate semantical objects for the discussion of properties of data, such as database dependencies or probabilities. There are instead notions of dependence - such as the causal dependencies arising from manipulationist theories of causation            (Pearl, Woodward) - which cannot be reduced to properties of data. These sorts of dependencies are meaningful in presence of a set of basic causal assumptions - a set of counterfactual statements, which are usually summarized by so-called structural equations.    However, theories of causation make a mixed use of observational and probabilistic notions (which concern data) and of causal notions. I will show how all these forms of reasoning can be modeled within one single semantical framework which simultaneously extends team semantics and structural equation models; and I will analyze some aspects of the logic of interventionist counterfactuals that emerges from this approach. (Joint work with Gabriel Sandu)

Wed 28.2.2018 12-14, C124
Miguel Moreno: \Sigma_1^1-complete quasi-orders in L

Wed 7.3.2018 12-14, C124
exam week

Wed 14.3.2018 12-14, C124
Miikka Vilander: TBA

Wed 21.3.2018 12-14, C124
TBA

Wed 28.3.2018 12-14, C124
TBA

Wed 4.4.2018 12-14, C124
Easter holiday

Wed 11.4.2018 12-14, C124
Oystein Linnebo TBA

Wed 18.4.2018 12-14, C124
Maria Hämeen-Anttila TBA

Wed 25.4.2018 12-14, C124
TBA

Wed 2.5.2018 12-14, C124
TBA

Wed 9.5.2018 12-14, C124
exam week

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