RT Journal Article
T1 Spectral Spaces in o-minimal and other NIP theories
A1 Baro González, Elías
A1 Fernando Galván, José Francisco
A1 Palacín Cruz, Daniel
AB We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil and Starchenko. In particular, we prove for definably compact groups that the space of closed points is homeomorphic to the space of infinitesimal types. We also prove that with the spectral topology the set of invariant types concentrated in a definably compact set is a normal spectral space whose closed points are the finitely satisfiable types. On the other hand, for arbitrary NIP structures we equip the set of invariant types with a new topology, called the honest topology. With this topology the set of invariant types is a normal spectral space whose closed points are the finitely satisfiable ones, and the natural retraction from invariant types onto finitely satisfiable types coincides with Simon’s FM retraction.
YR 2022
FD 2022-08-02
LK https://hdl.handle.net/20.500.14352/72650
UL https://hdl.handle.net/20.500.14352/72650
LA eng
NO Ministerio de Ciencia e Innovación
NO Comunidad de Madrid
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 26 abr 2025