Abstract
We generalize Keisler's omitting types theorem forL(Q) in the ℵ1-interpretation, to most cases in which Chang's two cardinal theorem applies. As an application we answer positively a question of Magidor and Malitz on the compactness of their logic in cardinalities higher than ℵ1.
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References
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Shelah, S. Models with second order properties. III. Omitting types forL(Q). Arch math Logik 21, 1–11 (1981). https://doi.org/10.1007/BF02011630
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DOI: https://doi.org/10.1007/BF02011630