Relatively exchangeable structures. Crane, H. & Towsner, H. *Journal of Symbolic Logic*, September, 2015. to appearArxiv abstract bibtex We study random relational structures that are \emphrelatively exchangeable–-that is, whose distributions are invariant under the automorphisms of a reference structure 𝔐. When 𝔐 has *trivial definable closure*, every relatively exchangeable structure satisfies a general Aldous–Hoover-type representation. If 𝔐 satisfies the stronger properties of *ultrahomogeneity* and *n-disjoint amalgamation property* (n-DAP) for every n≥1, then relatively exchangeable structures have a more precise description whereby each component depends locally on 𝔐.

@ARTICLE{2015arXiv150906733C,
author = {{Crane}, H. and {Towsner}, H.},
title = "{Relatively exchangeable structures}",
note={to appear},
journal={Journal of Symbolic Logic},
year = 2015,
month = sep,
urlarxiv={http://arxiv.org/abs/1509.06733},
abstract={We study random relational structures that are \emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure 𝔐. When 𝔐 has <i>trivial definable closure</i>, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If 𝔐 satisfies the stronger properties of <i>ultrahomogeneity</i> and <i>n-disjoint amalgamation property</i> (n-DAP) for every n≥1, then relatively exchangeable structures have a more precise description whereby each component depends locally on 𝔐.},
}

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