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Preprint Number 2222
2222. Elías Baro, José F. Fernando, and Daniel Palacín Spectral Spaces in o-minimal and other NIP theories E-mail: Submission date: 1 August 2022 Abstract: 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. Mathematics Subject Classification: Keywords and phrases: |

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