Jensen formulates classes of notions of forcing in [1]. We take subproper among those. This class is wider than proper, may differ from semiproper of Shelah and is iterable under the revised countable support a la Donder according to [1]. We formulate a class of notion of forcing whose definition involves less parameters than Jensen’s subproper and show that it iterates under a type of revised ...

Proof. If T were not complete, there would a sentence ψ such that neither ψ and ¬ψ would follow from T . But then T ∪ {ψ} and T ∪ {¬ψ} would have infinite models. Since λ ≥ |L|, both would actually have models of cardinality λ by the theorems of Skolem and Löwenheim. But these cannot be isomorphic, because they are not elementarily equivalent, contradicting the λ-categoricity of T . Theorem 1.2...