On a generalization of indiscernible sequences |
Pierre Touchard (TU Dresden) |
Tuesday, 2024-12-10 14:30 |
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Guingona and Hill introduced and studied a new hierarchy of dividing lines for first-order structures, denoted by (NC_K)_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. In 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. |