Tag Archives: Chang’s conjecture

Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract.  We prove that reflection of the coloring number of a graph is consistent with non-reflection of the chromatic number.  Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … Continue reading

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Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract.  We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading

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