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arXiv · 1307.4113

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

Vincent Guingona·Cameron Donnay Hill
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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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Vincent Guingona, Cameron Donnay Hill. 2013-07-15. On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension. https://arxiv.org/abs/1307.4113

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