Coloring infinite graphs and the Boolean prime ideal theorem |
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Authors: | H. Läuchli |
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Affiliation: | (1) E.T.H. Zürich, Switzerland |
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Abstract: | It is shown that the following theorem holds in set theory without AC: There is a functionG which assigns to each Boolean algebraB a graphG(B) such that (1) ifG(B) is 3-colorable then there is a prime ideal inB and (2) every finite subgraph ofG(B) is 3-colorable. The proof uses a combinatorial lemma on finite graphs. |
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