Determinacy and extended sharp functions on the reals, Part II: obtaining sharps from determinacy

AbstractFor several partial sharp functions # on the reals, we characterize in terms of determinacy, the existence of indiscernibles for several inner models of “#(r) 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 (r)=1#1γ+1(r) codes indiscernibles for L(r) [#11, #12,…, #1γ] and (β+1)#1γ+1(r)=#1γ+1(β#1γ+1(r)). We sho w that the existence of β#1γ(0) follows from the determinacy of (γ*Π01, (β−1)*Σ01)*+ games (whose definition we provide). Part I proves the converse