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- Title
CLASSIFICATION OF $\omega $ -CATEGORICAL MONADICALLY STABLE STRUCTURES.
- Authors
BODOR, BERTALAN
- Abstract
A first-order structure $\mathfrak {A}$ is called monadically stable iff every expansion of $\mathfrak {A}$ by unary predicates is stable. In this paper we give a classification of the class $\mathcal {M}$ of $\omega $ -categorical monadically stable structure in terms of their automorphism groups. We prove in turn that $\mathcal {M}$ is the smallest class of structures which contains the one-element pure set, is closed under isomorphisms, and is closed under taking finite disjoint unions, infinite copies, and finite index first-order reducts. Using our classification we show that every structure in $\mathcal {M}$ is first-order interdefinable with a finitely bounded homogeneous structure. We also prove that every structure in $\mathcal {M}$ has finitely many reducts up to interdefinability, thereby confirming Thomas' conjecture for the class $\mathcal {M}$.
- Subjects
AUTOMORPHISM groups; CLASSIFICATION; PERMUTATION groups; ISOMORPHISM (Mathematics)
- Publication
Journal of Symbolic Logic, 2024, Vol 89, Issue 2, p460
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2023.66