Note on extensions of Heyting's arithmetic by adding the ``creative subject''
type: Item
instance of: scholarly article
title: Note on extensions of Heyting's arithmetic by adding the ``creative subject''
zbMATH Open document ID: 0931.03072
author: Victor N. Krivtsov
published in: Archive for Mathematical Logic
publication date: 1999-10-05T00:00:00Z
review text: It is shown that the extension of Heyting's arithmetic HA by Kreisel's axioms for the creative subject [see \textit{A. S. Troelstra} and \textit{D. van Dalen}, Constructivism in mathematics. Vol. 1 (North-Holland, Amsterdam) (1988; Zbl 0653.03040), p. 236], with the induction schema restricted to arithmetical formulae, is conservative over HA. Some interesting generalizations of this result are considered in the last part of the paper. The proofs are based on the model-theoretic method.
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 1348069
zbMATH Keywords: Heyting arithmetic
zbMATH Keywords: creative subject
reviewed by: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: s001530050120
OpenAlex ID: W1970538682
DOI: 10.1007/S001530050120
description: scientific article; zbMATH DE number 1348069