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In [BKS15] examples of incomplete sentences are given with maximal models inmore than one cardinality. The question was raised whether one can find similarexamples of complete sentences.  In this paper we give examples of complete $L_{\omega_1,\omega}$-sentenceswith maximal models in more than one cardinality. From (homogeneous)characterizability of $\kappa$ we construct sentences with maximal models in$\kappa$ and in one of $\kappa^+, \kappa^\omega, 2^\kappa$ and more. Indeed,consistently we find sentences with maximal models in uncountably many distinctcardinalities.

Complete $\mathcal{L}_{\omega_1,\omega}$-Sentences with Maximal Models in Multiple Cardinalities