TL;DR
This paper establishes conditions under which a predicate in a complete theory is stably embedded, extending previous results to broader contexts involving NIP and finite rank, with implications for o-minimal structures.
Contribution
It provides new sufficient conditions for stable embeddedness of predicates in complete theories, generalizing prior work to include NIP and finite rank scenarios.
Findings
Predicate P with finite rank and NIP is stably embedded.
P being 1-stably embedded suffices for stable embeddedness.
Generalizes results for o-minimal structures to broader classes.
Abstract
We give sufficient conditions for a predicate P in a complete theory T to be stably embedded: P with its induced 0-definable structure has "finite rank", P has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson and Onshuus in the case where P is o-minimal in T.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · semigroups and automata theory