Inadmissible forcing (Q1102950)

The notion of a partial recursive function has been generalized by Normann and Moschovakis so that arbitrary sets are allowed as arguments. The authors use a forcing technique over transitive, recursively closed sets to prove the following: if L(\(\kappa)\) is countable, recursively closed, non \(\Sigma_ 1\)-admissible and the greatest cardinal of L(\(\kappa)\) has uncountable cofinality, then there is a subset S of an ordinal of L(\(\kappa)\) such that the recursive closure of S is equal to L(\(\kappa\),S). There is also an attempt to prove the converse and a list of problems concerning the structure of a recursive closure.