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Preprint Number 1645

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1645. Pedro Andrés Estevan and Itay Kaplan
Non-forking and preservation of NIP and dp-rank

Submission date: 10 September 2019


We investigate the question of whether the restriction of a NIP type p in S(B) which does not fork over A ⊆ B to A is also NIP, and the analogous question for dp-rank. We show that if B contains a Morley sequence I generated by p over A, then p|AI is NIP and similarly preserves the dp-rank. This yields positive answers for generically stable NIP types and the analogous case of stable types. With similar techniques we also provide a new more direct proof for the latter. Moreover, we introduce a general construction of “trees whose open cones are models of some theory” and in particular an inp-minimal theory DTR of dense trees with random graphs on open cones, which exemplifies a negative answer to the question.

Mathematics Subject Classification: 06A12, 03C45, 03C95

Keywords and phrases:

Full text arXiv 1909.04626: pdf, ps.

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