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Published online by Cambridge University Press: 12 March 2014
If A is an admissible set, let HC(A) = {x∣x ∈ A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the “real parts” of admissible sets and the analytical consequences of admissible set theory.
The research for this paper was supported by NSF Grant = MCS 76-07033. This paper accompanies a talk delivered by the author at the December, 1977 meeting of the Association for Symbolic Logic, Washington, D. C. The author wishes to thank the referee for his pointed and valuable suggestions.