Commutativity and self-reference
type: Item
instance of: scholarly article
title: Commutativity and self-reference
zbMATH Open document ID: 0528.03009
published in: Notre Dame Journal of Formal Logic
publication date: 1982-01-01T00:00:00Z
review text: A common occurrence in fixed point theory is the sharing of some fixed point by commuting operators. But, how common is (his occurrence in the arithmetical fixed point theory, i.e., in the theory of arithmetical self-reference? The author features the modal analysis of arithmetical self-reference as a tool to study this question and gives some observations with open problems from such a point of view. In the introduction, the author says: Though the results are not difficult, I think they do testify to the coherence of the modal theory. Moreover, through the exhibition of nontrivial differences between varying types of self-reference, they offer some indication of the possibility of a rich theory of arithmetical self-reference.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F99
zbMATH DE Number: 3837993
zbMATH Keywords: arithmetical self-reference
zbMATH Keywords: fixed point
zbMATH Keywords: commutativity
zbMATH Keywords: modal logic GL
zbMATH Keywords: modal analysis of arithmetical self-reference
zbMATH Keywords: commuting operators
author: Craig Smoryński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093870156
OpenAlex ID: W1974406212
DOI: 10.1305/NDJFL/1093870156
description: scientific article; zbMATH DE number 3837993