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March 2005 On the weak non-finite cover property and the n-tuples of simple structures
Evgueni Vassiliev
J. Symbolic Logic 70(1): 235-251 (March 2005). DOI: 10.2178/jsl/1107298518


The weak non-finite cover property (wnfcp) was introduced in [1] in connection with “axiomatizability” of lovely pairs of models of a simple theory. We find a combinatorial condition on a simple theory equivalent to the wnfcp, yielding a direct proof that the non-finite cover property implies the wnfcp, and that the wnfcp is preserved under reducts. We also study the question whether the wnfcp is preserved when passing from a simple theory T to the theory TP of lovely pairs of models of T (true in the stable case). While the question remains open, we show, among other things, that if (for a T with the wnfcp) TP is low, then TP has the wnfcp. To study this question, we describe “double lovely pairs”, and, along the way, we develop the notion of a “lovely n-tuple” of models of a simple theory, which is an analogue of the notion of a beautiful tuple of models of stable theories [2].


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Evgueni Vassiliev. "On the weak non-finite cover property and the n-tuples of simple structures." J. Symbolic Logic 70 (1) 235 - 251, March 2005.


Published: March 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1085.03026
MathSciNet: MR2119131
Digital Object Identifier: 10.2178/jsl/1107298518

Rights: Copyright © 2005 Association for Symbolic Logic


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Vol.70 • No. 1 • March 2005
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