Inadmissible forcing
type: Item
instance of: scholarly article
title: Inadmissible forcing
zbMATH Open document ID: 0645.03046
DOI: 10.1016/0001-8708(87)90028-4
author: Gerald E. Sacks
author: Theodore A. Slaman
published in: Advances in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03D65
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 4051601
zbMATH Keywords: E-recursive functions
zbMATH Keywords: forcing
zbMATH Keywords: recursively closed sets
MaRDI profile type: Publication
full work available at URL: 0001-8708(87)90028-4
OpenAlex ID: W4212885787
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description: scientific article; zbMATH DE number 4051601