Abstract

If C 1 , ..., C k are members of a certain class of suitable categories (which contains those arising from models with dimension), C = C 1 × ⋯ × C k , C' is a suitable category, F: C → C' is a partial recursive combinatorial functor satisfying a certain property (which, if C = C 1 , is that F is nonconstant) and U ∈ C, then (1) if FU is regressive so is U as is each U i , and (2) if FU is Dedekind then each U i is Dedekind