DOIAbstract
AbstractDuBose, D.A., Determinacy and the sharp function on the reals, Annals of Pure and Applied Logic 55 (1992) 237–263.We characterize in terms of determinacy, the existence of the least inner model of “every real has a sharp”. We let ♯1 be the (partial) sharp function on the reals and define two classes of sets, (Π01)∗ and (Π01)∗+, which lie strictly between ∪β<ω2(β-Π11) an d Δ(ω2-Π11). We show that the determinacy of (Π01)∗ follows from L[#1] ⊗xvR; “every real has a sharp”; and we show that the existence of indiscernibles for L[#1] is equivalent to a slightly determinacy hypothesis, the determinacy of (Π01)∗+
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