Salma Kuhlmann: Quasi-order-minimality: a uniform approach to o-minimality, C-minimality, p-minimality and variants thereof.

Set Theory and Topology seminar (BGU)

Time: Tuesday, December 29, 12:15-13:40.

Place: Seminar room -101, Math building 58.
Speaker: Salma Kuhlmann (Konstanz).
Title: Quasi-order- minimality: a uniform approach to o-minimality, C-minimality, p-minimality and variants thereof.
Abstract:  In the note “Quasi-Ordered Fields” by S. M. Fakhruddin [JPAA 45 (1987) 207-210] the author introduces the notion of a quasi-ordered (q.o.) field and shows the following dichotomy: a q.o. field is either an ordered field or a Krull valued field. We take this approach further to exhibit a theory of q.o. convex valuations. Classical results on (order) convex valuations can be reformulated for q.o. convex valuations in a natural way. In particular, this provides an elegant and uniform treatment of lifting of orderings, coarsening and composition of valuations. In this talk, I will explain the above, focusing on a new concept of “q.o.-minimality” generalizing several existing minimality notions.

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