# Does $2^{\mathfrak m}=2^{\mathfrak n}$ imply $\mathfrak m=\mathfrak n$? [duplicate]

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

• This is not a theorem of ZFC (unless ZFC happens to be inconsistent). – André Nicolas Jul 22 '13 at 19:16
• Do you bother searching the site? This has been asked at least twice before. – Asaf Karagila Jul 22 '13 at 19:17
• – Asaf Karagila Jul 22 '13 at 19:34
• @AsafKaragila: Thanks for the links! I honestly tried to find it, but I worded it in a different way, so couldn't find any. – mathreader Jul 22 '13 at 19:57

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