Set recursion and \(\Pi ^ 1_ 2\)-logic
type: Item
instance of: scholarly article
title: Set recursion and \(\Pi ^ 1_ 2\)-logic
zbMATH Open document ID: 0575.03034
DOI: 10.1016/0168-0072(85)90017-X
author: Jean-Yves Girard
author: Dag Normann
published in: Annals of Pure and Applied Logic
publication date: 1985-01-01T00:00:00Z
review text: This paper essentially has two parts. In an expository section central elements of \(\Pi^ 1_ 2\)-logic are introduced via denotation systems. The notion of a denotation system is a reformulation of the notion of a dilator. The well-founded decomposition of denotation systems is proved. The general theory is then applied on questions concerning set-recursion relativized to definable ordinal functions. If F:On\(\to On\) is set- recursive relative to a \(\Delta_ 1\)-function f:On\(\to On\), then there is a denotation system D such that F is bounded by a function G definable from f, D by recursion over a decomposition of D. A possible notion of general recursion over the decomposition of a denotation system is also discussed. The results of the paper have later been improved by J. Vauzeilles.
Mathematics Subject Classification ID: 03D60
Mathematics Subject Classification ID: 03F15
zbMATH DE Number: 3918358
zbMATH Keywords: pi-one-two logic
zbMATH Keywords: induction
zbMATH Keywords: denotation systems
zbMATH Keywords: dilator
zbMATH Keywords: decomposition
zbMATH Keywords: definable ordinal functions
MaRDI profile type: Publication
cites work: Q3960845
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full work available at URL: 0168-0072(85)90017-x
OpenAlex ID: W2046445497
description: scientific article; zbMATH DE number 3918358