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3 Clarified meaning of $\gamma$

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

2 added 192 characters in body

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?

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?

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# Is it consistent with ZFC that for all ordinals $\alpha, \beta < \omega$ it holds that $2^{\aleph_\alpha} = 2^{\aleph_\beta}$?

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?