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Preprint Number 1777

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1777. Santiago Cárdenas-Martín, Rafel Farré
Foundation ranks and supersimplicity

Submission date: 1st May 2020


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 as a foundation rank. In this way, SU, DU and D are foundation ranks based in the relation of dividing. We study the properties and the relations between these ranks. Next, we discuss the possible definitions of a supersimple type. This is a concept that it is not clear in the previous literature. In this paper we give solid arguments to set up a concrete definition of this concept and its properties. We also see that DU characterizes supersimplicity, while D not.

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Full text arXiv 2005.00520: pdf, ps.

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