Abstract.
A class K of structures is controlled if, for all cardinals λ, the relation of L ∞,λ-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
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Received: 23 September 1998 / Revised version: 6 July 1999 / Published online: 21 December 2000
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Laskowski, M., Shelah, S. The Karp complexity of unstable classes. Arch Math Logic 40, 69–88 (2001). https://doi.org/10.1007/s001530000047
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DOI: https://doi.org/10.1007/s001530000047