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Ioannis Souldatos [5]Ioannis A. Souldatos [2]
  1.  18
    Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence.Ioannis Souldatos - 2014 - Notre Dame Journal of Formal Logic 55 (4):533-551.
    This is the first part of a study on cardinals that are characterizable by Scott sentences. Building on previous work of Hjorth, Malitz, and Baumgartner, we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$ but no models of size $\kappa^{+}$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions, and countable products. We (...)
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  2.  2
    Complete Lω1,Ω‐Sentences with Maximal Models in Multiple Cardinalities.John Baldwin & Ioannis Souldatos - 2019 - Mathematical Logic Quarterly 65 (4):444-452.
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  3.  12
    Linear Orderings and Powers of Characterizable Cardinals.Ioannis Souldatos - 2012 - Annals of Pure and Applied Logic 163 (3):225-237.
  4.  3
    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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  5.  11
    Independently Axiomatizable ℒω1,Ω Theories.Greg Hjorth & Ioannis A. Souldatos - 2009 - Journal of Symbolic Logic 74 (4):1273-1286.
    In partial answer to a question posed by Arnie Miller [4] and X. Caicedo [2] we obtain sufficient conditions for an ℒω1,ω theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every ℒω1,ω theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.
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