arXiv subjects

Hirotaka Kikyo

Publications and source records attributed to Hirotaka Kikyo.

3 recordsLinked to original sources

arXiv2026

On chromatic number of countable graphs

This paper investigates when countable graphs have a finite or an infinite chromatic number through model theoretic methods. For Fraïssé limits, we show that instability forces the chromatic number to be infinite, yielding a complete classification of homogeneous graphs with a finite chromatic number. In contrast, Hrushovski construction always produces graphs of finite chromatic number, though the value can be made arbitrarily large. In tame settings -- such as stable graphs of $U$-rank one and graphs definable in o-minimal structures -- an infinite chromatic number necessarily yields arbitrarily large cliques. These results provide a unified framework connecting structural model theoretic properties with chromatic behavior.

math.LO↗

arXiv2000

The strict order property and generic automorphisms

If T is an model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.

math.LO↗

arXiv1998

Model companions of theories with an automorphism

For a theory $T$ in $L, T_σ$ is the theory of the models of $T$ with an automorphism $σ$. If $T$ is an unstable model complete theory without the independence property, then $T_σ$ has no model companion. If $T$ is an unstable model complete theory and $T_σ$ has the amalgamation property, then $T_σ$ has no model companion. If $T$ is model complete and has the fcp, then $T_σ$ has no model completion.

math.LO↗