Groups and fields with NTP2

Artem Chernikov*, Itay Kaplan, Pierre Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

NTP2 is a large class of first-order theories defined by Shelah generalizing simple and NIP theories. Algebraic examples of NTP2 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 NTP2 structures. Most importantly, we isolate a chain condition for definable normal subgroups and use it to show that any NTP2 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.

Original languageAmerican English
Pages (from-to)395-406
Number of pages12
JournalProceedings of the American Mathematical Society
Volume143
Issue number1
DOIs
StatePublished - 1 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014 American Mathematical Society.

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