Hideki will give a talk on “Infinite Adequacy Theorem through Coinductive Definitions” today at 14:00 as a part of our Theory seminar series and Kristijonas will speak on “Argumentation-enabled Explainable AI Applications” this Thursday at 15:00 at the CoFo.
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Ulrich Berger is currently attending the 3rd Workshop on Mathematical Logic and its Applications, Nancy, France, where he will present a talk on Extracting the Fan Functional.
As a part of our Theory Seminars, today we welcomed Ryota Akiyoshi from Waseda University, who gave a talk on Takeuti’s finitism.
Abstract: In this talk, we address several mathematical and philosophical issues of Gaisi Takeuti’s proof theory, who is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He furthered the realization of Hilbert’s program by formulating Gentzen’s sequent calculus for higher-oder logics, conjecturing that the cut-elimination holds for it (Takeuti’s conjecture), and obtaining several stunning results in the 1950-60’s towards the solution of his conjecture.
This talk consists of two parts. (1) To summarize Takeuti’s background and the argument of the well-ordering proof of ordinals up to ε0 , (2) To evaluate it on philosophical grounds. Also, we will explain several mathematical and philosophical issues to be solved. This is joint work with Andrew Arana.
Ulrich, Monika and Olga attended Hausdorff Trimester Program Types, Sets and Constructions in Bonn, Germany. During this research trip they have participated in the Constructive Mathematics workshop and had a chance to collaborate with partners from the past and existing projects, including COMPUTAL, CONRCON and CID.
Stephane Le Roux is visiting us from Darmstadt. Today he will give a talk on “Concurrent games and semi-random determinacy.”
Magne Haveraaen from the University of Bergen is visiting our Department in May-July 2018.
Ulrich and Olga visited Japan as part of the CID project in April 2018.
Amir Tabatabai and Rahele Jalali, both PhD students at the Institute of Mathematics of the Czech Academy of Sciences under the supervision of Pavel Pudlak, are visiting Swansea University 13 Nov – 6 Dec 2017.
Amir will give a talk on Computational Flows in Arithmetic on 16 November.
More information: A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among
them. In this talk we will explain the basics of the theory of computational
flows and how they make a sound and complete interpretation for bounded
theories of arithmetic. This property helps us to decompose a first order
arithmetical proof to a sequence of computational reductions by which we can
extract the computational content of the low complexity statements in some
bounded theories of arithmetic such as .