A subsystem of classical analysis proper to Takeuti's reduction method for \(\Pi ^ 1_ 1\)-analysis
type: Item
instance of: scholarly article
title: A subsystem of classical analysis proper to Takeuti's reduction method for \(\Pi ^ 1_ 1\)-analysis
zbMATH Open document ID: 0612.03024
author: Toshiyasu Arai
published in: Tsukuba Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author proposes a subsystem of classical analysis called AII (Axiom of Instantiation \(\forall \phi F(\phi)\supset F(V)\) with the Isolated formulae \(\forall \phi F(\phi))\) which is proved to be consistent following some methods of G. Gentzen and G. Takeuti. This result, together with related work by the author concerning derivability of transfinite induction in the system AII complements the proof of consistency of Takeuti's \((\Pi^ 1_ 1-CA)+(BI).\) The reader should be aware of some minor misprints, especially in the use of commas.
Mathematics Subject Classification ID: 03F25
Mathematics Subject Classification ID: 03F20
Mathematics Subject Classification ID: 03F07
zbMATH DE Number: 3989338
zbMATH Keywords: consistency proofs
zbMATH Keywords: subsystem of classical analysis
zbMATH Keywords: AII
zbMATH Keywords: Axiom of Instantiation
zbMATH Keywords: Isolated formulae
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160191
OpenAlex ID: W579673964
DOI: 10.21099/TKBJM/1496160191
description: scientific article; zbMATH DE number 3989338