Definable Minimal Collapse Functions at Arbitrary Projective Levels

Using a nonLaver modification of Uri Abraham’s minimal Δ ₃¹ collapse function, we define a generic extension $L[a]$ by a real a , in which, for a given n ≥ 3 , \ a \ is a lightface Π ₙ¹ singleton, a effectively codes a cofinal map ω → ω ₁L minimal over L , while every Σ ₙ¹ set X ⊆ ω is still constructible.