Valued difference fields and NTP2

Artem Chernikov (1) , Martin Hils (2)

1 ICJ - Institut Camille Jordan
2 ELM - Équipe de Logique Mathématique

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, we prove that a contractive sigma-henselian valued difference field of characteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference group) are NTP2. In addition, we demonstrate an analogous result for a possible refinement of NTP2 called resilience.

Mots clés: valued difference fields; NTP2; Ax-Kochen-Ershov; model theory

Domaines: Logique [math.LO]

Artem Chernikov, Martin Hils. Valued difference fields and NTP2. 2012. ⟨hal-00723415⟩