Groups and Fields in higher classification theoryOberseminar Logik

by Nadja Hempel (Düsseldorf)

Monday Jul 7, 2025, 5:00 PM → 6:00 PM Europe/Berlin

Endenicher Allee 60, Nebengebäude/N0-003 - Seminarraum (Mathezentrum)

A key goal in model theory is distinguishing between tame structures (e.g. the complex field) and wild structures (e.g. the ring of integers). This distinction was introduced by Shelah in the 1970s (Shelah’s Classification Theory) and is based on restricting combinatorial pattern given by definable binary relations. At the apex are the stable theories, such as the complex field, with two complementary extensions: NIP theories (including p-adic fields) and simple theories (such as pseudofinite fields).
In this talk, we briefly discuss fields whose theory is tame in the above sense. Afterwards, we leave the binary world, and introduce “n-ary” Classification theory. Instead of “controlling” 2-ary relation, we only assume that n-ary relations are tame. We give examples and discuss groups and fields within these classes of theories.