The equivalence of determinacy and iterated sharps

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Abstract
We characterize, in terms of determinacy, the existence of 0## as well as the existence of each of the following: 0###, 0####, 0#####,…. For κ Є ω, we define two classes of sets, and , which lie strictly between and . We also define 01# as# and in general, 0(k+1)# as (0k#)#. We then show that the existence of 0(k + 1)# is equivalent to the determinacy of as well as the determinacy of .

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