P.o.s adding no new branches
                     Sakae' Fuchino 
Abstract. 

A partial ordering P is said to be (kappa, lambda)-supported if, for any
V-generic G over P, every subset of kappa of size kappa contains a ground
model subset of cardinality lambda. We consider some elementary properties of
the class of (kappa, lambda)-supported p.o.s and their relation to some other
known klasses of p.o.s.