The degree of a \(\Sigma_ n\) cut
type: Item
instance of: scholarly article
title: The degree of a \(\Sigma_ n\) cut
zbMATH Open document ID: 0713.03028
DOI: 10.1016/0168-0072(90)90021-S
author: D. Kharzeev
published in: Annals of Pure and Applied Logic
publication date: 1990-01-01T00:00:00Z
review text: A reverse-recursion-theoretic investigation of how much strength is needed to prove the existence of minimal degrees or minimal pairs. Take any model of \(P^-+B\Sigma_ n+\neg I\Sigma_ n\) (n\(\geq 2)\), where \(P^-\) \(=\) Peano axioms without induction, \(B\Sigma_ n=\Sigma_ n\)- collection, and \(I\Sigma_ n=\Sigma_ n\)-induction. There exists a \(\Sigma_ n\)-definable cut in this model; let I be any such cut. The authors show that I and \(\emptyset^{n-1}\) form a minimal pair. They likewise show that, under appropriate coding assumptions, such a model also possesses a minimal degree.
reviewed by: Leon Harkleroad
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03D25
zbMATH DE Number: 4172967
zbMATH Keywords: reverse recursion theory
zbMATH Keywords: minimal degrees
zbMATH Keywords: minimal pairs
MaRDI profile type: Publication
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full work available at URL: 0168-0072(90)90021-s
OpenAlex ID: W2055041806
description: scientific article; zbMATH DE number 4172967