Foundation ranks and supersimplicity
Logic
2022-02-16 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2005.00520,
title = {Foundation ranks and supersimplicity},
author = {Santiago Cárdenas-Martín and Rafel Farré},
journal= {arXiv preprint arXiv:2005.00520},
year = {2022}
}