3 papers
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.LO2020
On the number of independent orders
Kota Takeuchi, Akito Tsuboi
We investigate a model theoretic invariant , which was introduced by Shelah in his famous book, and prove that is sub-additive. When is…
math.LO2001
Definability of initial segments
Saharon Shelah, Akito Tsuboi
We consider implicit definability of the standard part {0,1,...} in nonstandard models of Peano arithmetic (PA), and we ask whether there is a model of PA in which the standard par…