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Rosenthal compacta and NIP formulas

Volume 231 / 2015

Pierre Simon Fundamenta Mathematicae 231 (2015), 81-92 MSC: Primary 03C45; Secondary 54E52. DOI: 10.4064/fm231-1-5


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.


  • Pierre SimonCNRS, Université Lyon 1
    Institut Camille Jordan
    43 boulevard du 11 novembre 1918
    69622 Villeurbanne, France

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