Additivity of the dp-rank

Authors

Itay Kaplan, Alf Onshuus, Alexander Usvyatsov

Type: Preprint

Publication Date: 2011-09-07

Citations: 5

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Abstract

The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types, and discuss the possible relations between dp-rank and VC-density.

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arXiv (Cornell University)
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2007-01-01

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2011-08-12

Vincent Guingona , Cameron Donnay Hill

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Alexander Usvyatsov

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Alf Onshuus , Alexander Usvyatsov

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Itay Kaplan , Alexander Usvyatsov

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2005-04-10

Saharon Shelah

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Abstract We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has nonempty interior, and … Abstract We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has nonempty interior, and any theory of pure tree is dp-minimal.

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Vapnik–Chervonenkis Density in Some Theories without the Independence Property, II

2013-01-01

Matthias Aschenbrenner , Alf Dolich , Deirdre Haskell +2 more

We study the Vapnik–Chervonenkis (VC) density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite U-rank … We study the Vapnik–Chervonenkis (VC) density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite U-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.

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