期刊
ANNALS OF PURE AND APPLIED LOGIC
卷 166, 期 4, 页码 502-525出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apal.2014.11.007
关键词
op-dimension; op-rank; dp-rank; 2-rank; o-minimal
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. (C) 2014 Elsevier B.V. All rights reserved.
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