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Preprint Number 912

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912. John Baldwin, Ioannis Souldatos
Complete L_{ω_1,ω}-Sentences with Maximal Models in Multiple Cardinalities

Submission date: 26 August 2015.


In [BKS15] examples of incomplete sentences are given with maximal models in more than one cardinality. The question was raised whether one can find similar examples of complete sentences. In this paper we give examples of complete L_{ω_1,ω}-sentences with maximal models in more than one cardinality; indeed in countably many cardinalities.
The key new construction is a complete L_{ω_1,ω}-sentence with arbitrarily large models but with (κ^+,κ) models for every κ.

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Full text arXiv 1508.06620: pdf, ps.

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