Valued Difference Fields and Ntp

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, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference group) are NTP2. ∗ The first author was supported by the Marie Curie Initial Training Network in Mathematical Logic MALOA From MAthematical LOgic to Applications, PITN-GA-2009-238381. ∗∗ The second author was partially funded by the Agence Nationale de Recherche [MODIG, Projet ANR-09-BLAN-0047]. A substantial part of the research was carried out during the program ‘Model Theory and Applications’ at the Max Planck Institut für Mathematik in Bonn. The second author would like to thank the MPIM for its hospitality and support. Received August 31, 2012 and in revised form August 22, 2013