Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.
@article{1134397664,
author = {Pillay, Anand and Vassiliev, Evgueni},
title = {On Lovely Pairs and the ([?]y [?] P) Quantifier},
journal = {Notre Dame J. Formal Logic},
volume = {46},
number = {3},
year = {2005},
pages = { 491-501},
language = {en},
url = {http://dml.mathdoc.fr/item/1134397664}
}
Pillay, Anand; Vassiliev, Evgueni. On Lovely Pairs and the (∃y ∈ P) Quantifier. Notre Dame J. Formal Logic, Tome 46 (2005) no. 3, pp. 491-501. http://gdmltest.u-ga.fr/item/1134397664/