Theories with distal Shelah expansions
Gareth Boxall, Charlotte Kestner
TL;DR
This paper establishes that a complete first-order theory is distal if it has a model whose Shelah expansion's theory is distal, linking model properties to the overall theory's distality.
Contribution
It introduces a criterion connecting the distality of a theory to the distality of the Shelah expansion of a specific model.
Findings
A complete first-order theory is distal if it has a model with a distal Shelah expansion.
The theory of the Shelah expansion reflects the distality of the original theory.
Provides a new perspective on characterizing distality via Shelah expansions.
Abstract
We show that a complete first-order theory is distal provided it has a model such that the theory of the Shelah expansion of is distal.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology