English

Valued difference fields and NTP2

Logic 2013-08-27 v3

Abstract

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 sigma-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.

Keywords

Cite

@article{arxiv.1208.1341,
  title  = {Valued difference fields and NTP2},
  author = {Artem Chernikov and Martin Hils},
  journal= {arXiv preprint arXiv:1208.1341},
  year   = {2013}
}

Comments

Changes in v3: Section about resilience had been removed due to a mistake pointed out by the referee (and a corresponding conjecture had been added), the main theorem had been slightly generalized, overall presentation had been improved and some minor mistakes were corrected. Accepted for publication in the Israel Journal of Mathematics

R2 v1 2026-06-21T21:47:11.672Z