A negationless interpretation of intuitionistic theories. II
type: Item
instance of: scholarly article
title: A negationless interpretation of intuitionistic theories. II
zbMATH Open document ID: 0968.03073
DOI: 10.1023/A:1005207512630
author: Victor N. Krivtsov
published in: Studia Logica
publication date: 2001-02-06T00:00:00Z
review text: The author introduces negationless higher-order arithmetic, NAH, proves the translatability of HAH (intuitionistic higher-order arithmetic with product types, power types, and a type of natural numbers satisfying Heyting Arithmetic with full induction [cf. \textit{A. S. Troelstra} and \textit{D. van Dalen}, Constructivism in mathematics. An introduction. Vol. I, North-Holland, Amsterdam (1988; Zbl 0653.03040), pp. 168ff.] into NAH, and shows that NPC from Part I [Stud. Log. 64, No. 3, 323-344 (2000; Zbl 0964.03065)] is equivalent to a slight modification of the \(\Sigma\)-free fragment of Nelson's \(P_1\).
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03F35
zbMATH DE Number: 1513061
zbMATH Keywords: intuitionistic higher-order arithmetic
zbMATH Keywords: negationless higher-order arithmetic
reviewed by: Victor V. Pambuccian
MaRDI profile type: Publication
full work available at URL: a:1005207512630
OpenAlex ID: W1558782985
description: scientific article; zbMATH DE number 1513061