Abstract

DuBose, D.A., Determinacy and the sharp function on the reals, Annals of Pure and Applied Logic 55 237–263. We characterize in terms of determinacy, the existence of the least inner model of “every real has a sharp”. We let 1 be the sharp function on the reals and define two classes of sets, * and *+, which lie strictly between β<ω2 an d Δ. We show that the determinacy of * 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 *+.