On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension

Vincent Guingona,Cameron Donnay Hill

doi:10.1016/j.apal.2014.11.007

On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension

Vincent Guingona, Cameron Donnay Hill

Open Access

https://doi.org/10.1016/j.apal.2014.11.007

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Journal: Annals of Pure and Applied Logic	Publication Date: Dec 30, 2014
Citations: 10	License type: publisher-specific-oa

Affiliation: Ben-Gurion University of the Negev, Wesleyan University

#O-minimal Theories #Dimension Theory

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Abstract

In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories.

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