Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson.

Abstract.  We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number.  Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) is compatible with each of the following compactness principles: Rado’s conjecture, Fodor-type reflection, $\Delta$-reflection, Stationary-sets reflection, Martin’s Maximum,  and a generalized Chang’s conjecture.

This is accomplished by showing that, under GCH-type assumptions, instances of incompactness for the chromatic number can be derived from square-like principles that are compatible with large amounts of compactness.

Downloads:

[No arXiv entry][No published version][No entry on mathscinet]

This entry was posted in Compactness, Preprints and tagged , , , , , , , , , , , . Bookmark the permalink.

One Response to Reflection on the coloring and chromatic numbers

  1. saf says:

    Update Feb/2017: Added a new section, entitled “Realizing all closed intervals”.

       0 likes

Leave a Reply

Your email address will not be published. Required fields are marked *