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

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

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10.1305/ndjfl/1134397664

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Citations of this work

Weakly one-based geometric theories.Alexander Berenstein & Evgueni Vassiliev - 2012 - Journal of Symbolic Logic 77 (2):392-422.

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References found in this work

Lovely pairs of models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
The number of types in simple theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.
Paires de structures o-minimales.Yerzhan Baisalov & Bruno Poizat - 1998 - Journal of Symbolic Logic 63 (2):570-578.

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