Overspill and fragments of arithmetic
type: Item
instance of: scholarly article
title: Overspill and fragments of arithmetic
zbMATH Open document ID: 0677.03046
DOI: 10.1007/BF01622877
author: S. H. Smith
published in: Archive for Mathematical Logic
publication date: 1989-01-01T00:00:00Z
review text: The relations between overspill and the usual induction and collection schemata in arithmetic are considered. The author distinguishes strong \(\Gamma\)-overspill, \(\Gamma\)-overspill and weak \(\Gamma\)-overspill, where \(\Gamma\) is one of the following classes of formulas: \(\Sigma_ n\), \(\Pi_ n\), \(\Delta_ n\), \(E_ n\), \(U_ n\), and shows various relations between them.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03H15
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 4108761
zbMATH Keywords: overspill
zbMATH Keywords: induction
zbMATH Keywords: collection
MaRDI profile type: Publication
cites work: Gödel's Second incompleteness theorem for Q
cites work: Forcing, arithmetic, division rings
cites work: Completeness Theorems, Incompleteness Theorems and Models of Arithmetic
cites work: Parameter-Free Universal Induction
cites work: Bounded existential induction
full work available at URL: https://doi.org/10.1007/bf01622877
OpenAlex ID: W1967022936
description: scientific article; zbMATH DE number 4108761