Relatively exchangeable structures

2015/09/22 by Harry Crane, Crane, Harry, Henry Towsner +1 · 2 citations
Mathematics · #FOS: Mathematics #Logic (math.LO) #Probability (math.PR) #math.LO #math.PR

paper · pdf · doi:10.48550/arxiv.1509.06733

arxiv created 2015/10/01 · arxiv updated 2015/10/05

Abstract

We study random relational structures that are relatively exchangeable---that is, whose distributions are invariant under the automorphisms of a reference structure \mathfrakM. When \mathfrakM has \em trivial definable closure, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If \mathfrakM satisfies the stronger properties of \em ultrahomogeneity and \em 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 \mathfrakM.

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