Local classes and computable indexations
type: Item
instance of: scholarly article
title: Local classes and computable indexations
zbMATH Open document ID: 0665.03035
DOI: 10.1007/BF01978387
author: V. P. Dobritsa
published in: Algebra and Logic
publication date: 1987-01-01T00:00:00Z
review text: The author investigates some properties of constructive models in the sense of \textit{Yu. L. Ershov} [Decision problems and constructivizable models (Russian) (1980; Zbl 0495.03009)]. A notion of reducibility \(\leq_{\ell.c.}\), compatible with local classes, is introduced. The author shows that if a class \(K^*\) of constructive models has two computable indexings \(\alpha\) and \(\gamma\) such that \(\alpha\leq_{\ell.c.}\gamma\) then there exists a computable indexing \(\tau\) of the same class so that \(\alpha\) \(\nleq_{\ell.c.}\tau\), \(\gamma\) \(<_{\ell.c.}\tau\) and \(\tau\leq_{\ell.c.}\gamma.\) A sufficient condition under which a computable class K of constructive models has infinitely many incomparable indexings, is obtained. A number of other results are dispersed throughout the paper.
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 03C57
zbMATH DE Number: 4087653
zbMATH Keywords: constructive models
zbMATH Keywords: reducibility
zbMATH Keywords: local classes
zbMATH Keywords: computable indexings
MaRDI profile type: Publication
cites work: Q5573961
cites work: Q3322080
description: scientific article; zbMATH DE number 4087653