Truth in all of certain well‐founded countable models arising in set theory

Let M be a countable, transitive, &-model of ZF, V = L, i.e.-one of the models used by COHEN et al. [4] as the “starting point’’ for their independence results in set theory. In this model ramified languages L(T) or L ( T i , i E I) are defined to describe fully the models M (T) or M ( T i , i E I) used in independence results. We study the question-is {c E r 1 M ( T ) I= 0, VTf M-definable where r is the formulae of a certain bounded complexity. We show if r is 6 U2-unranked formulae it is, but if r is i Cnunranked formulae it is not.