Logic Seminar
Joseph Flenner
University of Notre Dame
Relative decidability of henselian valued fields.
Abstract: While logic has produced many results about the $p$-adics, among them a decision procedure due to Paul Cohen, the general theory of henselian valued fields presents an inherent difficulty: they are built on structures of arbitrary complexity in the residue field and value group. Ax-Kochen and Ersov, however, proved their completeness result for some henselian valued fields relative to the theories of the residue field and value group, and more recently, there have been some relative quantifier elimination theorems of Kuhlmann. In this spirit, we describe a structure of \emph{leading terms} associated to a valued field, and outline a proof of decidability for henselian valued fields of characteristic $0$ relative to the leading term structures.
seminar begins with tea
Tuesday October 20, 2009 at 4:00 PM in SEO 612