A certain generalization of SPFA to higher cardinals

Itay Neeman found in [6] a new way of iterating proper forcing notions and extended it in [7] to ℵ2. In [4] his construction for ℵ1 ([6]) was generalized to semi-proper forcing notions. We continue here [4] and extend the construction to higher cardinals still using nite conditions. In the nal model a weak form of SPFA will hold