Attempt of an axiomatic foundation of quantum mechanics and more general theories. III

Starting from axioms as physical as possible [1, 2, 3] about effects and ensembles, we shall investigate further consequences.Concerning part I and II [4, 5] the axioms can be so formulated as to be surveyed more easily.Besides, it is possible to prove some important theorems more simply.New structures of the lattice of decision effects are pointed out, leading in two subsequent papers at last to the final aim, the structure of Hilbert-space.