Complete L_ω_1,ω-Sentences with Maximal Models in Multiple Cardinalities release_sa6zy2querbq7mvscv7g3bbh3a

by John Baldwin, Ioannis Souldatos

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2018  

Abstract

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. From (homogeneous) characterizability of κ we construct sentences with maximal models in κ and in one of κ^+, κ^ω, 2^κ and more. Indeed, consistently we find sentences with maximal models in uncountably many distinct cardinalities.
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Date   2018-08-09
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arXiv  1508.06620v3
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