### Karp complexity and classes with the independence property

by Laskowski and Shelah. [LwSh:687]

Annals Pure and Applied Logic, 2003

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.

Back to the list of publications