A strongly non-Ramsey uncountable graph

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Title

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Department of Computer Science, Eötvös University, Múzeum krt. 6-8, 1088 Budapest, Hungary

It is consistent that there exists a graph X of cardinality

ℵ_{1}

such that every graph has an edge coloring with

ℵ_{1}

colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).

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