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RELATIVELY EXCHANGEABLE STRUCTURES

Published online by Cambridge University Press:  01 August 2018

HARRY CRANE  and
HENRY TOWSNER
HARRY CRANE
Affiliation:
DEPARTMENT OF STATISTICS & BIOSTATISTICS RUTGERS UNIVERSITY 110 FRELINGHUYSEN AVENUE, PISCATAWAY NJ 08854, USAE-mail:[email protected]: http://stat.rutgers.edu/home/hcrane
HENRY TOWSNER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF PENNSYLVANIA 209 SOUTH 33RD STREET, PHILADELPHIA PA 19104-6395, USAE-mail:[email protected]: http://www.math.upenn.edu/∼htowsner
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Abstract

We study random relational structures that are relatively exchangeable—that is, whose distributions are invariant under the automorphisms of a reference structure ${M}$. When ${M}$ is ultrahomogeneous and has trivial definable closure, all random structures relatively exchangeable with respect to $m$ satisfy a general Aldous–Hoover-type representation. If ${M}$ also satisfies the n-disjoint amalgamation property (n-DAP) for all $n \ge 1$, then relatively exchangeable structures have a more precise description whereby each component depends locally on ${M}$.

Keywords

03C0703C9860G09exchangeabilityAldous–Hoover theoremrelational structureFraïsse limitamalgamation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 416 - 442
Copyright
Copyright © The Association for Symbolic Logic 2018 

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