\(\Sigma_ 2\) induction and infinite injury priority arguments. II. Tame \(\Sigma_ 2\) coding and the jump operator
type: Item
instance of: scholarly article
title: \(\Sigma_ 2\) induction and infinite injury priority arguments. II. Tame \(\Sigma_ 2\) coding and the jump operator
zbMATH Open document ID: 0881.03023
DOI: 10.1016/0168-0072(96)00028-0
author: Yue Yang
author: C. T. Chong
published in: Annals of Pure and Applied Logic
publication date: 1998-01-26T00:00:00Z
review text: The authors consider models of the base theory \(PA^-\) that satisfy \(\Sigma_2\)-collection but not \(\Sigma_2\)-induction. They have shown elsewhere that such a model can contain no incomplete high r.e. degree. In this paper they prove that every such model must satisfy one of the following two conditions and that each condition is satisfied by some model: (a) all incomplete r.e. degrees are low; (b) there are exactly three degrees that are jumps of r.e. degrees. The proof proceeds by blocking for \(\Pi_2\) cuts.
Mathematics Subject Classification ID: 03D25
Mathematics Subject Classification ID: 03C62
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 1067505
zbMATH Keywords: recursively enumerable degree
zbMATH Keywords: jump operator
zbMATH Keywords: tame relation
zbMATH Keywords: \(\Sigma_ 2\)-induction
zbMATH Keywords: \(\Sigma_ 2\)-collection
zbMATH Keywords: blocking
reviewed by: Leon Harkleroad
MaRDI profile type: Publication
full work available at URL: 0168-0072(96)00028-0
OpenAlex ID: W2017850155
cites work: The degree of a \(\Sigma_ n\) cut
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description: scientific article; zbMATH DE number 1067505