Type decomposition in NIP theories

  • Pierre Simon

    University of California at Berkeley, USA
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A first order theory is NIP if all definable families of subsets have finite VC-dimension. We provide a justification for the intuition that NIP structures should be a combination of stable and order-like components. More precisely, we prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and an order-like quotient.

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Pierre Simon, Type decomposition in NIP theories. J. Eur. Math. Soc. 22 (2020), no. 2, pp. 455–476

DOI 10.4171/JEMS/926