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The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ0 or 2ℵ0. Morley showed that the number of countable models is finite or ℵ0 or ℵ1 or 2ℵ0, which solves the conjecture except for the case of ℵ1 models when the continuum hypothesis fails. For this remaining case, Robin Knight has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture. As of 2021, the counterexample has not been verified.

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  • Conjecture de Vaught (fr)
  • Vaught conjecture (en)
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  • La conjecture de Vaught est une conjecture mathématique proposée par Robert Lawson Vaught dans le champ de la théorie des modèles. Il s’agit de dire que l’ensemble des modèles dénombrables d’une théorie du premier ordre complète dans un langage dénombrable est soit fini, soit dénombrable, soit doté de la puissance du continu. Cette conjecture, malgré certaines avancées, reste un problème ouvert de la théorie des modèles. (fr)
  • The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ0 or 2ℵ0. Morley showed that the number of countable models is finite or ℵ0 or ℵ1 or 2ℵ0, which solves the conjecture except for the case of ℵ1 models when the continuum hypothesis fails. For this remaining case, Robin Knight has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture. As of 2021, the counterexample has not been verified. (en)
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  • La conjecture de Vaught est une conjecture mathématique proposée par Robert Lawson Vaught dans le champ de la théorie des modèles. Il s’agit de dire que l’ensemble des modèles dénombrables d’une théorie du premier ordre complète dans un langage dénombrable est soit fini, soit dénombrable, soit doté de la puissance du continu. Cette conjecture, malgré certaines avancées, reste un problème ouvert de la théorie des modèles. (fr)
  • The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ0 or 2ℵ0. Morley showed that the number of countable models is finite or ℵ0 or ℵ1 or 2ℵ0, which solves the conjecture except for the case of ℵ1 models when the continuum hypothesis fails. For this remaining case, Robin Knight has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture. As of 2021, the counterexample has not been verified. (en)
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