The equivalence of determinacy and iterated sharps

Journal of Symbolic Logic 55 (2):502-525 (1990)
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 k ∈ ω, we define two classes of sets, (k * Σ 0 1 ) * and (k * Σ 0 1 ) * + , which lie strictly between $\bigcup_{\beta and Δ(ω 2 -Π 1 1 ). We also define 0 1♯ as 0 ♯ and in general, 0 (k + 1)♯ as (0 k♯) ♯ . We then show that the existence of 0 (k + 1)♯ is equivalent to the determinacy of ((k + 1) * Σ 0 1 ) * as well as the determinacy of (k * Σ 0 1 ) * +
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DOI 10.2307/2274643
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An Extension of Borel Determinacy.Donald A. Martin - 1990 - Annals of Pure and Applied Logic 49 (3):279-293.
The Real Core Model and its Scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.
Determinacy and the Sharp Function on the Reals.Derrick Albert DuBose - 1992 - Annals of Pure and Applied Logic 55 (3):237-263.
Determinacy and the Sharp Function on the Reals.Derrick Albert DuBose - 1991 - Annals of Pure and Applied Logic 54 (1):59-85.

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