Is it consistent with ZFC that for all ordinals $\alpha, \beta < \omega$ it holds that $2^{\aleph_\alpha} = 2^{\aleph_\beta}$?
If yes, can the bound $\omega$ be increased here and how much?

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Update: In what sense the bound $\gamma$ can be made _arbitrarily_ high? If $\beta$ is the initial ordinal of $\beth_1$, then it cannot be that $2^{\aleph_0}=2^{\aleph_\beta}$, right?