Intuitionistic theory of algebraic systems and the Heyting-valued analysis
type: Item
instance of: scholarly article
title: Intuitionistic theory of algebraic systems and the Heyting-valued analysis
zbMATH Open document ID: 0793.03068
DOI: 10.1007/BF01978854
published in: Algebra and Logic
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/187569
review text: Given a ring \(f\) with a metric and a formula \(\varphi\Rightarrow\psi\) in the language of rings, we construct a translation \(\varphi^ +\Rightarrow \psi^ +\) such that the (classical) truth of the inference \(f\models (\varphi\Rightarrow \psi)\) (i.e., the inference \(\varphi_ f\Rightarrow \psi_ f\)) in the classical theory will imply, in a certain sense, the (intuitionistic) truth of the inference \(f\models (\varphi^ +\Rightarrow \psi^ +)\) [i.e., the inference \((\varphi^ +)_ f\Rightarrow (\psi^ +)_ f]\) in intuitionistic set theory.
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 59375
zbMATH Keywords: ring with a metric
zbMATH Keywords: classical truth
zbMATH Keywords: intuitionistic truth
zbMATH Keywords: language of rings
zbMATH Keywords: intuitionistic set theory
author: Vassily Lyubetsky
MaRDI profile type: Publication
OpenAlex ID: W1980096371
description: scientific article; zbMATH DE number 59375