Imaginaries in beautiful pairs

Anand Pillay; Evgueni Vassiliev

doi:10.1215/ijm/1258131051

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Home > Journals > Illinois J. Math. > Volume 48 > Issue 3 > Article

Fall 2004 Imaginaries in beautiful pairs

Anand Pillay, Evgueni Vassiliev

Illinois J. Math. 48(3): 759-768 (Fall 2004). DOI: 10.1215/ijm/1258131051

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Abstract

We prove that if $T = T^{eq}$ is a stable theory (without the finite cover property), then the theory $T_{P}$ of "beautiful pairs" eliminates imaginaries if and only if no infinite group is definable in a model of $T$.

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Anand Pillay. Evgueni Vassiliev. "Imaginaries in beautiful pairs." Illinois J. Math. 48 (3) 759 - 768, Fall 2004. https://doi.org/10.1215/ijm/1258131051