Model theory of difference fields with an additive character on the fixed field
Tuesday, 3.12.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Motivated by work of Hrushovski on pseudofinite fields with an additive character we investigate the theory ACFA+ which is the model companion of the theory of difference fields with an additive character on the fixed field working in (a mild version of) continuous logic. Building on results by Hrushovski we can recover it as the characteristic 0 asymptotic theory of the algebraic closure of finite fields with the Frobenius-automorphism and the standard character on the fixed field. We characterise 3-amalgamation in ACFA+ and obtain that ACFA+ is simple as well as a description of the connected component of the Kim-Pillay group. If time permits we present some results on higher amalgamation.\n
On a generalization of indiscernible sequences
Tuesday, 10.12.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Guingona and Hill introduced and studied a new hierarchy of dividing lines for first-order structures, denoted by (NCK)K , where K ranges in the theorie of ultrahomogeneous omega-categorical Ramsey structures. In a subsequent paper, Guigonna, Hill and Scow give a characterisation in terms of (generalised) K-indiscernible sequences.\nIn this talk, I will present a joint work with Nadav Meir and Aris Papadopoulos, in which we develop around these notions of K-indiscernibility. In particular, we will answer (negatively) a question posed by Guingona and Hill about the linearity of the NC_K hierarchy. As an application, we will also see that the ordered random graph admits a unique proper Ramsey reduct, namely the linear order.