The equational compatibility problem for the real line

. Walter Taylor proved recently that there is no algorithm for deciding of a finite set of equations whether it is topologically compatible with the real line in the sense that it has a model with universe and with basic operations which are all continuous with respect to the usual topology of the r...

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Bibliographic Details
Published in:Algebra universalis 2008-12, Vol.59 (3-4), p.257-275
Main Author: McNulty, George F.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:. Walter Taylor proved recently that there is no algorithm for deciding of a finite set of equations whether it is topologically compatible with the real line in the sense that it has a model with universe and with basic operations which are all continuous with respect to the usual topology of the real line. Taylor’s account used operation symbols suitable for the theory of rings with unit together with three unary operation symbols intended to name trigonometric functions supplemented finally by a countably infinite list of constant symbols. We refine Taylor’s work to apply to single equations using operation symbols for the theory of rings with unit supplemented by two unary operation symbols and at most one additional constant symbol.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-008-2025-9