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DP-MINIMALITY: INVARIANT TYPES AND DP-RANK

Published online by Cambridge University Press:  12 December 2014

PIERRE SIMON
PIERRE SIMON*
Affiliation:
UNIVERSITÉ DE LYON; CNRS UNIVERSITÉ LYON 1 INSTITUT CAMILLE JORDAN UMR5208 43 BOULEVARD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX, FRANCEE-mail: pierre.sim85@gmail.com
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Abstract

This paper has two parts. In the first one, we prove that an invariant dp-minimal type is either finitely satisfiable or definable. We also prove that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium directionality.

In the second part, we study dp-rank in dp-minimal theories and show that it enjoys many nice properties. It is continuous, definable in families and it can be characterised geometrically with no mention of indiscernible sequences. In particular, if the structure expands a divisible ordered abelian group, then dp-rank coincides with the dimension coming from the order.

Keywords

model theoryNIPdp-minimaldp-rank
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1025 - 1045
Copyright
Copyright © The Association for Symbolic Logic 2014 

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References

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