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2007 The Vaught Conjecture: Do Uncountable Models Count?
John T. Baldwin
Notre Dame J. Formal Logic 48(1): 79-92 (2007). DOI: 10.1305/ndjfl/1172787546

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.

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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

Information

Published: 2007
First available in Project Euclid: 1 March 2007

zbMATH: 1125.03025
MathSciNet: MR2289898
Digital Object Identifier: 10.1305/ndjfl/1172787546

Subjects:
Primary: 03C15, 03C45

Rights: Copyright © 2007 University of Notre Dame

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