On the construction of simple first-order formulae without recursive models

• Autores: Egon Börger
• Localización: Coloquio sobre lógica simbólica: Madrid, febrero 1975, 1976, ISBN 84-600-0531-3, págs. 7-24
• Idioma: inglés
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• Resumen

  • The paper is about solutions of the well known problems from Hilbert-Bernays whether every satisfiable closed formula of the restricted lower predicate calculus admits recursive models. Aanderaa's method is presented which associates formulae to register machine programs in such a way that the formula is the axiom of an essentially undecidable theory resp. satisfiable but without recursive models if the machine program enumerates two recursively inseparable sets. A simplification of Aanderaa's formulae brings their decision problems still closer to the corresponding stop problems of the machine programs and results in a more direct and technically less involved realization of the basic idea.[...]