The Karp complexity of unstable classes |
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| Authors: | MC Laskowski S Shelah |
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| Institution: | (1) Department of Mathematics, University of Maryland, College Park, MD 20742, USA. e-mail: mcl@math.umd.edu, US;(2) Department of Mathematics, Hebrew University of Jerusalem, 91904, Jerusalem, Israel and Department of Mathematics, Rutgers University, IL |
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| 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 the class of doubly transitive linear orders
is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
Received: 23 September 1998 / Revised version: 6 July 1999 / Published online: 21 December 2000 |
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| Keywords: | Mathematics Subject Classification (2000): 03C |
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