Séminaire Logique mathématique ICJ

# Exponentiation is easy to avoid (some- times). (Exposé dans le cadre des rencontres Franco-Colombiennes.)

## by Pablo Cubides (Université de Caen)

Europe/Paris
4ème étage salle 435 (ENS Lyon Site Monod)

### 4ème étage salle 435

#### ENS Lyon Site Monod

Description

A celebrated theorem of Chris Miller states that if R is an o-minimal expansion of the field of real numbers then either R is polynomially bounded or the exponential function is definable in R. After introducing an analogue of o-minimality for expansions of algebraically closed valued fields (called C- minimality), the aim of the talk is to show that every C-minimal expansion of a valued field (K, v) having value group Q is polynomially bounded. In particular, we obtain that any C-minimal expansion of valued fields like $C_p$, $F^{alg} ((t^Q ))$ are polynomially bounded. This is a joint work with Françoise Delon.

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