Groups in NTP2

HENSELIAN VALUED FIELDS AND inp-MINIMALITY

“…the theory VFA 0 of a non-standard Frobenius on an algebraically closed valued field of characteristic zero [CH14]. See also [CKS15] and [HO15] for some general results about groups and fields definable in NTP 2 structures.…”

“…Other algebraic examples of NTP 2 structures were identified recently, including bounded pseudo real closed and pseudo p-adically closed fields [15], certain model complete multivalued fields [13] and certain valued difference fields, e.g., the theory VFA 0 of a nonstandard Frobenius on an algebraically closed valued field of characteristic zero [6]. See also [7] and [12] for some general results about groups and fields definable in NTP 2 structures.…”

On Amalgamation in NTP2 Theories and Generically Simple Generics

“…A couple of important facts are known: over extension bases, forking equals dividing ( [CK12]) and the non-forking ideal is S1 ( [BYC14]). In addition, some theorems on groups generalizing similar results for simple and NIP theories have been proved: Hempel and Onshuus [HO17] construct definable envelopes for abelian and solvable subgroups; [CKS15] studies chain conditions and [MOS16] sets the foundations for the theory of definably amenable NTP 2 groups. More recently [KS17] explores analogues of some NIP-like phenomena.…”

Some NIP-like phenomena in NTP$_{2}$

“…Under the assumption of groups or fields, more has been done. See for example [CKS15] (about groups and fields in general NTP 2 ), [HO17] (about definable envelopes of subgroups), and more recently [MOS16] (about groups definable in bounded PRC fields).…”