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

For 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 # 1 0=1# 1 0 be the identity function on the reals. Inductively define the partial sharp function, β# 1 γ+1, on the reals so that # 1 γ+1 ( r)=1# 1 γ+1( r) codes indiscernibles for L( r) [# 1 1, # 1 2,…, # 1 γ] and ( β+1)# 1 γ+1( r)=# 1 γ+1( β# 1 γ+1( r)). We sho w that the existence of β# 1 γ(0) follows from the determinacy of (γ* Π 0 1, ( β−1)* Σ 0 1) * + games (whose definition we provide). Part I proves the converse.