Tag Archives: Ostaszewski square

Same Graph, Different Universe

Posted on December 13, 2014 by Assaf Rinot in categories: Infinite Graphs, Publications.

Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading →

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Hedetniemi’s conjecture for uncountable graphs

Posted on July 25, 2013 by Assaf Rinot in categories: Infinite Graphs, Publications.

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal κ, there exist graphs G and H of size and chromatic number κ, for which the tensor product graph G×H is countably chromatic. … 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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The Ostaszewski square, and homogeneous Souslin trees

Posted on May 18, 2011 by Assaf Rinot in categories: Publications, Souslin Hypothesis, Squares and Diamonds.

Abstract: Assume GCH and let λ denote an uncountable cardinal. We prove that if ◻λ holds, then this may be  witnessed by a coherent sequence ⟨Cα∣α<λ+⟩ with the following remarkable guessing property: For every sequence ⟨Ai∣i<λ⟩ … Continue reading →

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