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Morley’s number of countable models

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Title: Morley’s number of countable models
Authors: Blanck, Rasmus
Issue Date: 10-May-2011
Degree: Student essay
Abstract: A theory formulated in a countable predicate calculus can have at most 2א0 nonisomorphic countable models. In 1961 R. L. Vaught [9] conjected that if such a theory has uncountably many countable models, then it has exactly 2א0 countable models. This would of course follow immediately if one assumed the continuum hypothesis to be true. Almost ten years later, M. Morley [5] proved that if a countable theory has strictly more than א1 countable models, then it has 2א0 countable models. This l... more
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