Karp complexity and classes with the independence property
نویسندگان
چکیده
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 [4]).
منابع مشابه
The Karp complexity of unstable classes
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 the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
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عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 120 شماره
صفحات -
تاریخ انتشار 2003