The definable (p,q)-theorem for distal theories
Gareth Boxall, Charlotte Kestner
TL;DR
This paper proves that in distal NIP theories, non-dividing formulas over a model are part of a definable family, extending the understanding of definability in model theory.
Contribution
It establishes a definable (p,q)-theorem for distal theories, answering a specific open question in model theory.
Findings
Non-dividing formulas are part of a definable family in distal NIP theories
The result extends the definability properties known in distal theories
Addresses a question posed by Chernikov and Simon
Abstract
Answering a special case of a question of Chernikov and Simon, we show that any non-dividing formula over a model M in a distal NIP theory is a member of a consistent definable family, definable over M.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Homotopy and Cohomology in Algebraic Topology