Coloring infinite graphs and the Boolean prime ideal theorem

@article{Luchli1971ColoringIG,
  title={Coloring infinite graphs and the Boolean prime ideal theorem},
  author={H. L{\"a}uchli},
  journal={Israel Journal of Mathematics},
  year={1971},
  volume={9},
  pages={422-429}
}
  • H. Läuchli
  • Published 1971
  • Mathematics
  • Israel Journal of Mathematics
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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