Karp complexity and classes with the independence property

2003/03/27 by Michael C. Laskowski, Saharon Shelah · 1 citation
Mathematics · #math.LO

paper · pdf

published as Annals of Pure and Applied Logic, 120 (2003), 263-283

arxiv created 2003/03/27 · arxiv updated 2009/11/30

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 no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled.

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