Karp complexity and classes with the independence property
Authors:
M. C. Laskowski and S. Shelah
Affiliation:
a Department of Mathematics, University of Maryland, College Park, MD 20742, USA
b Department of Mathematics, Hebrew University of Jerusalem, Israel
c Department of Mathematics, Rutgers University, USA
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 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 (see Arch. Math. Logic 40 (2001) 69–88).