Given a set $X$ is it provable in $\mathsf{ZF}$ that there is a binary operation $\ast: X\times X\to X$ such that $(X,\ast)$ is a group?
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asked Nov 28, 2014 at 11:54
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$\begingroup$ No, as this is equivcalent to AC. See mathoverflow.net/questions/12973/… This is thus a duplicate. $\endgroup$– user9072Commented Nov 28, 2014 at 12:11
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$\begingroup$ Oh - it is a duplicate. I'm sorry. $\endgroup$– Dominic van der ZypenCommented Nov 28, 2014 at 12:11
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$\begingroup$ And in any case, you need to assume $X$ is nonempty! $\endgroup$– Arturo MagidinCommented Nov 28, 2014 at 22:30
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