The Karp complexity of unstable classes

by Laskowski and Shelah. [LwSh:560]
Archive for Math Logic, 2001
A class K of structures is controlled if, for all cardinals lambda, the relation of L_{infty, lambda}-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 omega-independence property is not controlled.

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