Essentially disjoint families, conflict free colorings and Shelah's Revised GCH

Lajos Soukup

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arXiv · 1207.1971

Essentially disjoint families, conflict free colorings and Shelah's Revised GCH

Lajos Soukup

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Abstract

Using Shelah's revised GCH theorem we prove that if mu =kappa for all b from B has a conflict-free colorings with kappa colors. Putting together these results we obtain that if mu =beth_omega for all b from B has a conflict-free colorings with beth_omega colors. To yield the above mentioned results we also need to prove a certain compactness theorem concerning singular cardinals.

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Lajos Soukup. 2012-07-09. Essentially disjoint families, conflict free colorings and Shelah's Revised GCH. https://arxiv.org/abs/1207.1971

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