DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS.

Using a nonLaver modification of Uri Abraham's minimal Δ₃¹ 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 → ω₁^L minimal over L , while every Σ_n¹ set X ⊆ ω is still constructible. [ABSTRACT FROM AUTHOR]