The isomorphism property versus the special model axiom

Abstract

AbstractThis paper answers some questions of D. Ross in [R]. In §1, we show that some consequences of the ℵ1- or ℵ1-special model axiom in [R] cannot be proved by the κ-isomorphism property for any cardinal κ. In §2, we show that with one exception, the ℵ0-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In §3, we improve a result in [R] by showing that the κ-special model axiom is equivalent to the ℵ0-special model axiom plus κ-saturation.