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Seminar

DDC - Valuation Theory: Ordered fields dense in their real closure and definable convex valuations December 09, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Salma Kuhlmann (Universität Konstanz)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Video

Ordered Fields Dense In Their Real Closure And Definable Convex Valuations

Abstract/Media

Title: Ordered fields dense in their real closure and definable convex valuations.

Joint work with Lothar Sebastian Krapp and Gabriel Lehericy.

Abstract:

In this talk I present our model and valuation theoretic study of the class of ordered fields which are dense in their real closure. I will show how we can use this to determine definable henselian valuations on ordered fields, in the language of ordered rings. In light of our results, we re-examine a conjecture of Shelah (specialised to ordered fields) and provide an example limiting its valuation theoretic conclusions.

 

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

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Ordered Fields Dense In Their Real Closure And Definable Convex Valuations

H.264 Video 25221_28735_8675_Ordered_Fields_Dense_in_Their_Real_Closure_and_Definable_Convex_Valuations.mp4