Lothar Sebastian Krapp (Konstanz): Valuations Definable in the Language of Ordered Rings

Donnerstag, 05.12.2019 11:00 im Raum SR 1D
Mathematik und Informatik

Let L_r := {+,-,*,0,1} be the language of rings and let L_or := {+,-,*,0,1,<} be the language of ordered rings. The study of definable valuations (i.e. valuations whose corresponding valuation ring is a definable set) in certain fields is motivated by the general analysis of definable subsets of fields as well as by recent conjectures on the classification of NIP fields. There is a vast collection of results giving conditions on L_r-definability of henselian valuations in a given field, many of which are from recent years (cf. [Fehm-Jahnke19]). So far, not much seems to be known about L_or-definable valuations in ordered fields. Since L_or is a richer language than L_r, it is natural to expect further definability results in the language of ordered rings. In my talk, I will outline some progress in the study of L_or-definable valuations from my joint work with S. Kuhlmann and G. Lehéricy. In this regard, I will present sufficient topological conditions on the value group and the residue field of a henselian valuation v on an ordered field such that v is L_or-definable. Moreover, I will show how the study of L_or-definable valuations connects to ordered fields dense in their real closure as well as above mentioned conjectures regarding NIP fields. All valuation and model theoretic notions will be introduced.

Angelegt am Montag, 02.12.2019 12:00 von pfeifer
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