Kolmogorov complexity and symmetric relational structures

TL;DR

This paper explores how partitions of Fraïssé limits of finite relational structures, encoded by Kolmogorov-random sequences, preserve the limit properties of these structures, linking algorithmic randomness with model theory.

Contribution

It demonstrates that Kolmogorov-random partitions of Fraïssé limits maintain the structures' limit properties, connecting algorithmic randomness with structural model theory.

Findings

Random partitions preserve the Fraïssé limit property

Kolmogorov randomness encodes structural partitions

Structural properties are invariant under random partitions

Abstract

We study partitions of Fra\"{\i}ss\'{e} limits of classes of finite relational structures where the partitions are encoded by infinite binary sequences which are random in the sense of Kolmogorov, Chaitin and Solomonoff. It is shown that partition by a random sequence of a Fra\"{\i}ss\'{e} limit preserves the limit property of the object.