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Talks during the spring term 2015

Wed 14.1.2015 12-14, C124
Jouko Väänänen: On Continuum Hypothesis in the inner model C*

Wed 21.1.2015 12-14, C124
Miguel Moreno: On the reducibility of the isomorphism relation I

Wed 28.1.2015 12-14, C124
Miguel Moreno: On the reducibility of the isomorphism relation II

Wed 4.2.2015 12-14, C124
Andrés Villaveces (Bogotá): Model theory and modular invariants

Abstract: the model theory of the classical j invariant has been studied by A. Harris: he has isolated geometrical conditions that make a categoricity analysis in the style of Zilber possible. At the same time, I have worked in quantum variants of the j invariant together with T. Gendron: we have isolated various sheaf constructions that allow calculations of versions of the j invariant for reals. This uses non-standard analysis, combined with a little logic of sheaves. I plan to provide a panorama of these works (Harris, and my joint work with Gendron) on j invariants.

Wed 11.2.2015 12-14, C124
Menachem Magidor: Omitting types in continous logic is hard (joint work with Ilijas Farah)

Wed 18.2.2015 12-14, C124
Carlos di Prisco: Semiselective coideals and forcing

Wed 25.2.2015 12-14, C124
Cancelled.

Wed 4.3..2015 12-14, C124
Spring break (exam week)

Wed 11.3.2015 12-14, C124
Juha Kontinen: A van Benthem theorem for modal team semantics

Wed 18.3.2015 12-14, C124
Cancelled.

Wed 25.3.2015 12-14, C124
Jouko Väänänen: Inner models from extended logics

Wed 1.4.2015 12-14, C124
Vadim Kulikov: Fractal knots and turbulent equivalence relations

Wed 8.4.2015 12-14, C124
Easter holiday

Wed 15.4.2015 12-14, C124
Jouko Väänänen: On the Logic of Approximate Dependence

Wed 22.4.2015 12-14, C124
Gianluca Paolini: A Non-Elementary Plane

Wed 29.4.2015 12-14, C124
Andy Arana (Urbana): Purity and content

Abstract: Roughly, a solution to a problem, or a proof of a theorem, is pure if it draws only on what is 'close' or 'intrinsic' to that problem or theorem. On one precisification of purity that we have called 'topical purity', closeness of theorem and proof is to be measured in terms of content. In brief, a proof is topically pure if it draws only on what belongs to the content of the theorem it is proving, i.e. on what must be grasped in order to understand that theorem. But how is this 'belonging' determined? In this talk I consider this question in light of examples from number theory (prime number theorem), logic (Gödel's incompleteness theorems), and geometry (Desargues' theorem). Each case considers theorems whose content may be understood in multiple ways: the prime number theorem as a result of elementary arithmetic or of analysis; the incompleteness theorems as a result of arithmetic or set theory; and Desargues' theorem as a result of plane projective or spatial projective geometry. Negotiating these different ways of identifying a theorem's content is crucial for making sense of purity, yet there is at present no systematic way to do so. I will discuss this as a problem for investigation going forward.

 

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