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Logic and Computation Seminar

Friday, September 2, 2022 - 4:30pm

Franz-Viktor Kuhlmann

University of Szczecin


University of Pennsylvania


NOTE: This is joint with the Algebra Seminar. Tea/coffee/refreshments will be served at 3:00-3:30pm and 4:15-4:30pm in the Math Lounge, DRLB 4th floor.

Part II: Decidability of Laurent series fields over finite fields, 4:30-5:15 PM

In 1965 Ax -- Kochen, and Ershov, proved the decidability of the elementary theory of the fields of p-adic numbers. The problem for their counterpart in positive characteristic, the Laurent series fields over finite fields, is still open. I will explain what is meant by "elementary theory" and which tools can be used to prove decidability. The task can be reduced to proving embedding lemmas for valued function fields, which I will describe. This is what the decidability problem under discussion has in common with the local uniformization problem. In analogy to the local uniformization problem, our theory of defect has led to new model theoretic results about certain classes of valued fields in positive characteristic.

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