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  • Author or Editor: P. Komjáth x
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Abstract  

It is consistent that there exists an uncountably chromatic triple system which does not contain two triples with two common points or circuits of lengths 3, 5.

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Abstract  

We determine a class of triple systems such that each must occur in a triple system with uncountable chromatic number that omits

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{T}_0$$ \end{document}
(the unique system consisting of two triples on four vertices). This class contains all odd circuits of length ≧ 7. We also show that consistently there are two finite triple systems such that they can separately be omitted by uncountably chromatic triple systems but not both.

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Authors: P. Komjáth and S. Shelah
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Without Abstract

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It is consistent that there exists a set mappingF with ß<F(ß, a)<a for ß + 2 = a >w 2 with no uncountable free sets.

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