On reflection and non-reflection of countable list-chromatic number of graphs (Aspects of Descriptive Set Theory)
Sakaé Fuchino, Hiroshi Sakai · Institutional Repositories DataBase (IRDB) · 2012
It is known that the reflection cardinal of countable chromatic number of graphs is fairly large.This stands in contrast with the situation of the countable coloring number whose reflection cardinal is less or equal to that of the Fodor-type Reflection Principle and hence can be consistently $\aleph_{2}$ .Applying a theorem of Peter Komj\'ath, it can be shown that the reflection of countable list-chromatic number behaves consistently similarly to the reflection of countable chromatic number but it can also behave consistently like the reflection of countable coloring number.Moreover, the Fodor-type Reflection Principle does not decide in which way the reflection of countable list-chromatic number behaves.