2020/05/01 by Santiago Cárdenas-Martín, Cárdenas-Martín, Santiago, Rafel Farré +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2005.00520
openalex publication_date 2020/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.