Addendum to ``Countable algebra and set existence axioms''
type: Item
instance of: scholarly article
title: Addendum to ``Countable algebra and set existence axioms''
zbMATH Open document ID: 0575.03039
DOI: 10.1016/0168-0072(85)90020-X
author: Harvey M. Friedman
author: Stephen G. Simpson
author: Rick L. Smith
published in: Annals of Pure and Applied Logic
publication date: 1985-01-01T00:00:00Z
review text: The authors admit that (one direction of) the proof of Theorem 3.1 of the above paper (see Zbl 0575.03038) is flawed; they retract the remark following that proof, which was based on the flawed part; and they provide an alternate proof of the theorem, strengthening it at the same time by adding to the two equivalent conditions a third one: (3) Every countable commutative ring with a unit has a radical ideal. Finally they fill the two question marks on top of page 148 by results from the literature.
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03E30
Mathematics Subject Classification ID: 03B30
zbMATH DE Number: 3918363
zbMATH Keywords: weakest possible subsystem
zbMATH Keywords: second-order arithmetic
zbMATH Keywords: encoding of structures
zbMATH Keywords: reverse mathematics
zbMATH Keywords: comprehension
Wikidata QID: Q114684044
reviewed by: Gebhard Fuhrken
MaRDI profile type: Publication
cites work: Countable algebra and set existence axioms
cites work: Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
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description: scientific article; zbMATH DE number 3918363