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Complete L_ω_1,ω-Sentences with Maximal Models
in Multiple Cardinalities
release_sa6zy2querbq7mvscv7g3bbh3a
by
John Baldwin, Ioannis Souldatos
Released
as a article
.
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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1508.06620v3
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