The Karp complexity of unstable classes

2000/11/21 by M. Laskowski, Michael C. Laskowski, Saharon Shelah +2
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #math.LO

paper · pdf · doi:10.48550/arxiv.math/0011167

published as Arch. Math. Logic 40 No. 2 (2001) 69--88

arxiv created 2000/11/21 · 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 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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