On dp-minimal ordered structures
P. Simon
TL;DR
This paper explores properties of dp-minimal ordered structures, establishing that dp-minimal groups are almost abelian, infinite sets have interior in divisible groups, and pure trees are dp-minimal, contributing to the understanding of their model-theoretic behavior.
Contribution
It provides new results on the structure and properties of dp-minimal ordered structures, including groups and trees, expanding the theoretical framework of dp-minimality.
Findings
Dp-minimal groups are abelian-by-finite-exponent
In divisible ordered dp-minimal groups, infinite sets have non-empty interior
Pure trees are dp-minimal
Abstract
We show some basic facts about dp-minimal ordered structures. The main results are : dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Fuzzy and Soft Set Theory