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On Relations between Structures

Theoria 32 (3):172-185 (1966)

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  1. In memoriam: Per Lindström.Jouko Väänänen & Dag Westerståhl - 2010 - Theoria 76 (2):100-107.
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  • Zum Entscheidungsproblem für Theorien in Logiken mit Monadischen Verallgemeinerten Quantoren.H. Herre & A. G. Pinus - 1978 - Mathematical Logic Quarterly 24 (19-24):375-384.
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  • Applications of vaught sentences and the covering theorem.Victor Harnik & Michael Makkai - 1976 - Journal of Symbolic Logic 41 (1):171-187.
    We use a fundamental theorem of Vaught, called the covering theorem in [V] (cf. theorem 0.1 below) as well as a generalization of it (cf. Theorem $0.1^\ast$ below) to derive several known and a few new results related to the logic $L_{\omega_1\omega}$. Among others, we prove that if every countable model in a $PC_{\omega_1\omega}$ class has only countably many automorphisms, then the class has either $\leq\aleph_0$ or exactly $2^{\aleph_0}$ nonisomorphic countable members (cf. Theorem $4.3^\ast$) and that the class of countable (...)
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