A Metric Version Of Schlichting'S Theorem

JOURNAL OF SYMBOLIC LOGIC（2020）

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摘要

If F is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with F. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

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关键词

Schlichting's Theorem, uniformly commensurable, close-knit family, continuous logic, invariant

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