Abstract
We present here a refinement of the method of Jensen coding [7] and apply it to the study of admissible ordinals. An ordinal α is recursively inaccessible if it is both admissible and the limit of admissible ordinals. Solovay asked if it is consistent to have a real R such that the R-admissible ordinals equal the recursively inaccessible ordinals. This is a problem in class forcing as any real in a set generic extension of L must preserve the admissibility of a final segment of the admissible ordinals. Our main theorem provides an affirmative solution to Solovay's problem.
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