A minimal predicative set theory
type: Item
instance of: scholarly article
title: A minimal predicative set theory
zbMATH Open document ID: 0816.03023
author: Franco Montagna
author: Antonella Mancini
published in: Notre Dame Journal of Formal Logic
publication date: 1995-07-20T00:00:00Z
review text: The authors choose a very weak set theory, denoted by N, having just the following axioms: (1) \(\emptyset\) exists, and (2) for any two sets \(x\), \(y\), \(x\cup \{y\}\) exists, and prove that Robinson's arithmetic Q is interpretable in N. This is to be understood as a reasonable reduction from the point of view of Hilbert's Program, which continues analogous work of E. Nelson. The proof of the interpretability of Q into N is given through a large number of steps which are a bit difficult to follow. A finistic proof of Herbrand consistency of N is also given.
reviewed by: Athanassios Tzouvaras
Mathematics Subject Classification ID: 03E70
zbMATH DE Number: 721964
zbMATH Keywords: weak set theory
zbMATH Keywords: Robinson's arithmetic
zbMATH Keywords: interpretability
zbMATH Keywords: Herbrand consistency
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1094061860
OpenAlex ID: W2077162222
DOI: 10.1305/NDJFL/1094061860
description: scientific article; zbMATH DE number 721964