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Daniel Palacín (Universidad Complutense de Madrid)

Models and Sets Seminar
Wednesday 29 November 2023, 4.00 PM

The space of types with a spectral topology

Note time change: 4 pm GMT

Influenced by results in real algebraic geometry, Pillay pointed out in 1988 that the space of types of an o-minimal expansion of a real closed field admits a spectral topology. With this topology, this space is quasi-compact and $T_0$, yet not Hausdorff. Nonetheless, the subspace of all closed points turns out to be quasi-compact and Hausdorff. The purpose of this talk is to present some results on the spectral space of types for o-minimal and more generally NIP theories. This is joint work with Elías Baro and José Fernando.