On the consistency of the \(\Delta_1^1\)-CA fragment of Frege's Grundgesetze
type: Item
instance of: scholarly article
title: On the consistency of the \(\Delta_1^1\)-CA fragment of Frege's Grundgesetze
zbMATH Open document ID: 1012.03059
DOI: 10.1023/A:1019919403797
author: Fernando Ferreira
author: Kai Frederick Wehmeier
published in: Journal of Philosophical Logic
publication date: 2003-06-13T00:00:00Z
review text: It is well known that Frege's system in the ``Grundgesetze der Arithmetik'' is formally inconsistent. Richard Heck proved that the fragment of Frege's system obtained by restricting the comprehension schema to predicative formulae is consistent and conjectured that the more encompassing \(\Delta_{1}^{1}\)-comprehension schema would already be inconsistent . In the paper under review it is shown that this is not the case.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 1870147
zbMATH Keywords: consistency
zbMATH Keywords: fragment of Frege's Grundgesetze
zbMATH Keywords: \(\Delta_{1}^{1}\)-comprehension schema
MaRDI profile type: Publication
cites work: Q4110995
cites work: On a consistent subsystem of Frege's Grundgesetze
cites work: First-order Frege theory is undecidable
cites work: The Consistency of predicative fragments of frege’s grundgesetze der arithmetik
cites work: Q4001935
cites work: On the consistency of the first-order portion of Frege's logical system
cites work: Consistent fragments of \textit{Grundgesetze} and the existence of non-logical objects
full work available at URL: a:1019919403797
OpenAlex ID: W1986689580
description: scientific article; zbMATH DE number 1870147