Re: An exercise in set theory: How high do we get by autonomously iterating the powerset operation?

Aatu Koskensilta wrote:

As everyone and his sister knows, in Zermelo set theory the stages of the
cumulative hierarchy we can provably reach are all below the omega + omega'th
level. In terms of the conception of the world of sets given by the cumulative
hierarchy this doesn't really make much sense; there are well-orderings
within V_omega + omega of order type way beyond omega + omega, and it thus seems
a bit odd why we should not iterate the "set of" operation more than omega +
omega times.

This line of thought suggests the following mathematical question. What is the
least ordinal alpha with the property that alpha > omega and if there is a
well-ordering of type beta in V_alpha, beta < alpha? (Hint: consider the
fixed point of a suitable ordinal function.)

Sorry you had no takers, not in the ng at least. So what's the answer?

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