On the \({\mathbb{I}}\)-condition
The \({\mathbb{I}}\)-condition on forcing notions which implies that the forcing it satisfies does not add reals, was introduced by \textit{S. Shelah} [Proper forcing (1982; Zbl 0495.03035), Chapter XI {\S}2]. Some examples of forcing notions that can iterate while preserving the \({\mathbb{I}}\)- condition are presented and a new sufficient condition on forcing is formulated for the revised countable support iterations preserving the \({\mathbb{I}}\)-condition.
scientific article; zbMATH DE number 3891349