Abstract

For several partial sharp functions # on the reals, we characterize in terms of determinacy, the existence of indiscernibles for several inner models of “# exists for every real r”. Let #10=1#10 be the identity function on the reals. Inductively define the partial sharp function, β#1γ+1, on the reals so that #1γ+1 =1#1γ+1 codes indiscernibles for L [#11, #12,…, #1γ] and #1γ+1=#1γ+1). We sho w that the existence of β#1γ follows from the determinacy of *Σ01)*+ games . Part I proves the converse