The 42 reducts of the random ordered graph
Manuel Bodirsky, Michael Pinsker, Andr\'as Pongr\'acz
TL;DR
This paper classifies all the reducts of the random ordered graph, a unique countable homogeneous structure, up to first-order interdefinability, expanding understanding of its logical and structural properties.
Contribution
It provides a complete classification of the reducts of the random ordered graph, a significant step in understanding its automorphism group and definable relations.
Findings
Identifies all reducts up to first-order interdefinability.
Characterizes the automorphism groups of these reducts.
Enhances understanding of the structure's logical complexity.
Abstract
The random ordered graph is the up to isomorphism unique countable homogeneous linearly ordered graph that embeds all finite linearly ordered graphs. We determine the reducts of the random ordered graph up to first-order interdefinability.
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