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  1. Complete Lω1,ω‐sentences with maximal models in multiple cardinalities.John Baldwin & Ioannis Souldatos - 2019 - Mathematical Logic Quarterly 65 (4):444-452.
    In [5], 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 ‐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 and more. Indeed, consistently we find sentences with maximal models in uncountably many distinct cardinalities.
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  • Kurepa trees and spectra of $${mathcal {L}}{omega 1,omega }$$ L ω 1, ω -sentences.Dima Sinapova & Ioannis Souldatos - 2020 - Archive for Mathematical Logic 59 (7-8):939-956.
    We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a single \-sentence \ that codes Kurepa trees to prove the following statements: The spectrum of \ is consistently equal to \ and also consistently equal to \\), where \ is weakly inaccessible.The amalgamation spectrum of \ is consistently equal to \ and \\), where again \ is weakly inaccessible. This is the first example of an \-sentence whose spectrum and amalgamation spectrum are consistently both right-open and (...)
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  • Disjoint amalgamation in locally finite aec.John T. Baldwin, Martin Koerwien & Michael C. Laskowski - 2017 - Journal of Symbolic Logic 82 (1):98-119.
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