Michael C. Laskowski, Saharon Shelah
Published 2000-11-21Version 1
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.
Set theory with a proper class of indiscernibles
Karp complexity and classes with the independence property
Coding and reshaping when there are no sharps
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