Abstract

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- and Δ. We show that the determinacy of * follows from L[#1] “every reak has a sharp”; and we show that the existence of indiscernibles for L[#1] is equivalent to a slightly stronger determinacy hypothesis, the determinacy of *+