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The Karp complexity of unstable classes

Michael C. Laskowski·Saharon Shelah
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Abstract

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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Michael C. Laskowski, Saharon Shelah. 2000-11-21. The Karp complexity of unstable classes. https://arxiv.org/abs/math/0011167

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