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Suppose $\mathfrak m$ and $\mathfrak n$ are infinite cardinals. Does $2^{\mathfrak m}=2^{\mathfrak n}$ imply $\mathfrak m=\mathfrak n$?

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This is independent of ZFC. It is implied by GCH for example, but there exist models where (say) $2^{\aleph_0}=2^{\aleph_1}=\aleph_2$.

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  • $\begingroup$ Thank you for the answer! Could you possibly direct me to any source that states this fact? $\endgroup$ – mathreader Jul 22 '13 at 19:28
  • $\begingroup$ Never mind, I got the links provided above. $\endgroup$ – mathreader Jul 22 '13 at 19:58

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