Model Theory Seminar: n-dependent Groups and Fields

Seminar | September 4 | 2-3 p.m. | 891 Evans Hall

 Nadja Hempel, UCLA

 Department of Mathematics

1-dependent theories better known as NIP theories are the first class of the hierarchy of n-dependent structures. The random n-hypergraph is the canonical object which is n-dependent but not (n-1)-dependent. Thus the hierarchy is strict. But one might ask if there are any algebraic objects (groups, rings, fields) which are strictly n-dependent for every n? We will start by introducing the n-dependent hierarchy and present the known results on n-dependent groups and (valued) fields. These were (more or less) inspired by the above question.