Church's thesis from the point of view of provability interpretation
type: Item
instance of: scholarly article
title: Church's thesis from the point of view of provability interpretation
zbMATH Open document ID: 0681.03041
author: N. A. Pankrat'ev
published in: Moscow University Mathematics Bulletin
publication date: 1988-01-01T00:00:00Z
review text: The paper considers a natural extension of one usual way to provide a provability interpretation for the intuitionistic logical language in the arithmetical language as follows. For each arithmetical formula F let tr(F) be a result of prefixing \(\square\) to each subformula of F, and let \(F^*\) be the result of an interpretation \(\square Q\) as Q\&Pr[Q] in a formula tr(F). Here Pr[Q] is the standard formula of provability of Q in Peano Arithmetic. The paper demonstrates that if F is one of the following formal versions of Church's thesis: CT, CT!, ECT, nCT, then the arithmetic formula \(F^*\) is false in the standard model of arithmetic.
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F25
zbMATH DE Number: 4114624
zbMATH Keywords: modal logic
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: provability interpretation
zbMATH Keywords: Church's thesis
reviewed by: Sergei Artemov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4114624