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

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?