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Open Access Publications from the University of California

Groups and fields with NTP2

  • Author(s): Chernikov, A
  • Kaplan, I
  • Simon, P
  • et al.

NTP is a large class of first-order theories defined by Shelah generalizing simple and NIP theories. Algebraic examples of NTP structures are given by ultra-products of p-adics and certain valued difference fields (such as a non-standard Frobenius automorphism living on an algebraically closed valued field of characteristic 0). In this note we present some results on groups and fields definable in NTP structures. Most importantly, we isolate a chain condition for definable normal subgroups and use it to show that any NTP field has only finitely many Artin-Schreier extensions. We also discuss a stronger chain condition coming from imposing bounds on burden of the theory (an appropriate analogue of weight) and show that every strongly dependent valued field is Kaplansky. 2 2 2 2

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