Algebra universalis

, Volume 59, Issue 3–4, pp 257–275 | Cite as

The equational compatibility problem for the real line

  • George F. McNulty


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 \({\mathbb{R}}\) 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.

2000 Mathematics Subject Classification:

Primary: 08B05 Secondary: 03D35, 22A30, 26B40 

Keywords and phrases:

Equational compatibility Hilbert’s Tenth Problem algorithmic unsolvability topological algebra 


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Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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