Mathematics > Logic
[Submitted on 10 Sep 2019 (v1), last revised 14 Dec 2019 (this version, v2)]
Title:Non-forking and preservation of NIP and dp-rank
View PDFAbstract:We investigate the question of whether the restriction of a NIP type $p\in S(B)$ which does not fork over $A\subseteq B$ 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 $p\restriction AI$ 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.
Submission history
From: Pedro Andrés Estevan [view email][v1] Tue, 10 Sep 2019 17:07:47 UTC (49 KB)
[v2] Sat, 14 Dec 2019 19:57:27 UTC (51 KB)
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