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On the weak non-finite cover property and the n-tuples of simple structures

Published online by Cambridge University Press:  12 March 2014

Evgueni Vassiliev
Evgueni Vassiliev*
Affiliation:
Wilkes Honors College, Florida Atlantic University, 5353 Parkside Drive, Jupiter, Florida 33458, USA, E-mail: evassili@fau.edu
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Abstract

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].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 235 - 251
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

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