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Preprint Number 1076

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1076. Douglas Ulrich
The Number of Atomic Models of Uncountable Theories
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Submission date: 26 July 2016

Abstract:

We show there exists a complete theory in a language of size continuum possessing a unique atomic model which is not constructible. We also show it is consistent with ZFC + ℵ_1 < 2^{ℵ_0} that there is a complete theory in a language of size ℵ_1 possessing a unique atomic model which is not constructible. Finally we show it is consistent with ZFC + ℵ_1 < 2^{ℵ_0} that for every complete theory T in a language of size ℵ_1, if T has uncountable atomic models but no constructible models, then T has 2^{ℵ_1} atomic models of size ℵ_1.

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Full text arXiv 1607.07833: pdf, ps.


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