The equational compatibility problem for the real line

• Autores: George F. McNulty
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 59, Nº. 3-4, 2008, págs. 257-275
• Idioma: inglés
• DOI: 10.1007/s00012-008-2025-9
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• Resumen

  • 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.