7 citations · 9 across the 4 of their papers we have counts for
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Rank axioms and supersimplicity
Santiago Cárdenas-Martín, Rafel Farré
Just as Lascar's notion of abstract rank axiomatizes the U-rank, we propose axioms for the ranks and , the foundation ranks of dividing and forking. We study the relat…
Foundation ranks and supersimplicity
Santiago Cárdenas-Martín, Rafel Farré
We introduce a new foundation rank based in the relation of dividing between partial types. We call DU to this rank. We also introduce a new way to define the D rank over formulas…
A rank based on Shelah trees
Santiago Cárdenas-Martín, Rafel Farré
We define a global rank for partial types based in a generalization of Shelah trees. We prove an equivalence with the depth of a localized version of the constructions known as div…
Strong ordered Abelian groups and dp-rank
Rafel Farré
We provide an algebraic characterization of strong ordered Abelian groups: An ordered Abelian group is strong iff it has bounded regular rank and almost finite dimension. Moreover,…