Abstract
We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality κ. We prove that one can define a graph G whose chromatic number is >κ, while the chromatic number of every subgraph G′⫅G, |G′|<|G| is ≦κ. The main case is κ=ℵ0.
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The author thanks Alice Leonhardt for the beautiful typing. The author would like to thank the Israel Science Foundation for partial support of this research (Grant no. 1053/11). Publication 1006.
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Shelah, S. On incompactness for chromatic number of graphs. Acta Math Hung 139, 363–371 (2013). https://doi.org/10.1007/s10474-012-0287-3
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DOI: https://doi.org/10.1007/s10474-012-0287-3