Rosenthal compacta and NIP formulas

Pierre Simon (1)

1 AGL - Algèbre, géométrie, logique

We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about phi-types for phi NIP. In particular, we show that if M is a countable model, then an M-invariant phi-type is Borel definable. Also the space of M-invariant phi-types is a Rosenthal compactum, which implies a number of topological tameness properties.

Mots clés: Rosenthal compacta; NIP; model theory

Domaines: Logique [math.LO]

Pierre Simon. Rosenthal compacta and NIP formulas. Fundamenta Mathematicae, 2015, 231, pp.81--92. ⟨10.4064/fm231-1-5⟩. ⟨hal-01027443v2⟩