Tag Archives: incompactness

11th Young Set Theory Workshop, June 2018

Posted on June 30, 2018 by Assaf Rinot in categories: Invited Talks.

I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading →

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MFO workshop in Set Theory, February 2017

Posted on February 19, 2017 by Assaf Rinot in categories: Invited Talks.

I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading →

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Reflection on the coloring and chromatic numbers

Posted on December 18, 2016 by Assaf Rinot in categories: Compactness, Infinite Graphs, Publications.

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) … Continue reading →

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Chromatic numbers of graphs – large gaps

Posted on April 12, 2013 by Assaf Rinot in categories: Compactness, Infinite Graphs, Publications.

Abstract. We say that a graph G is (ℵ0,κ)-chromatic if Chr(G)=κ, while Chr(G′)≤ℵ0 for any subgraph G′ of G of size <|G|. The main result of this paper reads as follows. If  ◻λ+CHλ holds for a given uncountable cardinal λ, … Continue reading →

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