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math.LO2026
On chromatic number of countable graphs
Hirotaka Kikyo, Koitaro Nakaura, Akito Tsuboi
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…
math.LO2000
The strict order property and generic automorphisms
Hirotaka Kikyo, Saharon Shelah
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.LO1998★ 1 cited
Model companions of theories with an automorphism
Hirotaka Kikyo
For a theory in is the theory of the models of with an automorphism . If is an unstable model complete theory without the independence property, then …