# Mathematical Sciences Research Institute

Home » DDC - Valuation Theory: Ordered fields dense in their real closure and definable convex valuations

# 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: Decidability, definability and computability in number theory: Part 1 - Virtual Semester 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