Model Theory of Homogeneous D-sets
Felipe Estrada, John Goodrick
TL;DR
This paper investigates the model-theoretic properties of D-sets, focusing on ultrahomogeneity, indiscernible sequences, and dp-minimality, providing new classifications and characterizations within this mathematical framework.
Contribution
It introduces new characterizations of ultrahomogeneity and distal properties in colored D-sets, and establishes that all quantifier-eliminating colored D-sets are dp-minimal.
Findings
Characterization of ultrahomogeneity in colored D-sets
Classification of unbounded order-indiscernible sequences
Proof that quantifier-eliminating colored D-sets are dp-minimal
Abstract
We explore several model-theoretic aspects of D-sets, which were studied in detail by Adeleke and Neumann. We characterize ultrahomogeneity in the class of colored D-sets and classify unbounded order-indiscernible sequences in such structures. We use these results to provide a characterization of distal colored D-sets and prove that all colored D-sets with quantifier elimination are dp-minimal.
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Taxonomy
TopicsRough Sets and Fuzzy Logic · Data Management and Algorithms