Infinitary logic, uncountable models, and counterexamples to the Vaught conjecture
by Greg Hjorth
Abstract: Assuming there is an infinitary sentence which provides a counterexample to the Vaught conjecture, one can show that there must be a counterexample which has no model of cardinality bigger than the first uncountable cardinal. Although the result is purely model theoretic, the proof its self relies almost exclusively on methods from descriptive set theory.
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