On Lovely Pairs and the (∃ y ∈ P ) Quantifier

Notre Dame Journal of Formal Logic 46 (4):491-501 (2005)

Abstract
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
Keywords simple theory   low   pair
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DOI 10.1305/ndjfl/1134397664
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