Pablo Andujar Guerrero (University of Leeds) – The open core of NTP2 topological structures

The open core of a structure is the reduct generated by the open definable sets. Tame topological structures (e.g. o-minimal) are inter-definable with their open core. Structures such as M = (ℝ, <, +, ℚ) are wild in the sense that they define a dense co-dense set. Still, M is NIP and its open core is o-minimal. In this talk we push forward the thesis that the open core of an NTP₂ (a generalization of NIP) topological structure is tame. Our main result is that, under suitable conditions, the open core has quantifier elimination, and its definable functions are generically continuous.