Unimodularity unified
Dar\'io Garc\'ia, Frank Olaf Wagner
TL;DR
This paper investigates unimodularity in model theory, analyzing its properties within stationary types, introducing variants for definable sets, and establishing equivalences in non-multidimensional theories with strongly minimal types.
Contribution
It introduces variants of unimodularity for definable sets and explores their relationships, providing new insights into unimodularity's behavior in specific theories.
Findings
All notions of unimodularity coincide in non-multidimensional theories with strongly minimal types.
Unimodularity is localized to complete stationary types and analyzed within this context.
Relationships between different variants of unimodularity are established.
Abstract
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied. In particular, it is shown that all notions coincide for non-multidimensional theories where the dimensions are associated to strongly minimal types.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms