### The Vaught Conjecture: Do Uncountable Models Count?

John T. Baldwin
Source: Notre Dame J. Formal Logic Volume 48, Number 1 (2007), 79-92.

#### 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.

First Page:
Primary Subjects: 03C15, 03C45
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1172787546
Digital Object Identifier: doi:10.1305/ndjfl/1172787546
Mathematical Reviews number (MathSciNet): MR2289898
Zentralblatt MATH identifier: 1125.03025

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