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math.LO2013
On VC-minimal fields and dp-smallness
Vincent Guingona
In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show th…
math.LO2013
On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension
Vincent Guingona, Cameron Donnay Hill
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-o…