Abstract
We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{ω₁,ω}$-types. The following result is new. Theorem: If a first-order theory is a counterexample to the Vaught Conjecture then it has 2\sp ℵ₁ models of cardinality ℵ₁.
Citation
John T. Baldwin. "The Vaught Conjecture: Do Uncountable Models Count?." Notre Dame J. Formal Logic 48 (1) 79 - 92, 2007. https://doi.org/10.1305/ndjfl/1172787546
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