Epistemic set theory
type: Item
instance of: scholarly article
title: Epistemic set theory
zbMATH Open document ID: 0688.03043
author: William N. Reinhardt
published in: Notre Dame Journal of Formal Logic
publication date: 1988-01-01T00:00:00Z
review text: The modal provability operator is axiomatized in the context of set theory so that it provides a framework for consideration of the Post- Turing thesis. Following the ideas of Gödel and Kripke, the author first defines on ZFC a theory of concepts, on which the axioms for the modal provability operator are formulated. In this framework, then, the strong form of the Post-Turing thesis is formulated, not as a schema but as a sentence. The author also suggests that it is possible in this framework to deal with such a notion as ordinal notations that involve essentially both constructive and non-constructive notions.
Mathematics Subject Classification ID: 03F50
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03E70
Mathematics Subject Classification ID: 03F15
zbMATH DE Number: 4127204
zbMATH Keywords: epistemic set theory
zbMATH Keywords: constructivity
zbMATH Keywords: nonconstructivity
zbMATH Keywords: modal provability operator
zbMATH Keywords: Post-Turing thesis
zbMATH Keywords: theory of concepts
zbMATH Keywords: ordinal notations
reviewed by: Osamu Sonobe
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093637872
OpenAlex ID: W2054131045
DOI: 10.1305/NDJFL/1093637872
description: scientific article; zbMATH DE number 4127204