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Karp complexity and classes with the independence property |
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| Authors: | M C Laskowski and S Shelah |
| Institution: | 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). |
| Keywords: | Independence property Coding graphs Non-structure theorems |
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