We investigate the list-chromatic number of infinite graphs. It is easy to see that Chr(X) ≤ List(X) ≤ Col(X) for each graph X. It is consistent that List(X) = Col(X) holds for every graph with Col(X) infinite. It is also consistent that for graphs of cardinality ℵ 1, List(X) is countable iff Chr(X) is countable.
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