Independence results

Abstract

Abstract We prove independence results concerning the number of nonisomorphic models (using the S -chain condition and S -properness) and the consistency of “ there is a universal linear order of power ℵ 1 ”. Most of these results were announced in [Sh 4], [Sh 5]. In subsequent papers we shall prove an analog f MA for forcing which does not destroy stationary subsets of ω 1 investigate -properness for various filters and prove the consistency with G.C.H. of an axiom implying SH (for ℵ 1 ), and connected results.