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The transitivity of Kim-independence

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The transitivity of Kim-independence

The class of NSOP_1 theories contains the simple theories and many interesting non-simple theories, such as the omega-free PAC fields or generic vector spaces with a non-degenerate bilinear form. With Itay Kaplan, we introduced Kim-independence which agrees with non-forking independence within the simple theories and shares many of its nice properties within the simple NSOP_1 context. One very basic roadblock in lifting simplicity theory to the NSOP_1 setting, however, was transitivity: a free extension of a free extension should still be a free extension. This is almost immediate for non-forking extensions in a simple theory, but becomes more involved for free extensions in the sense of Kim-independence. We will describe and motivate the basic theory, and then discuss our recent proof of transitivity. This is joint with Itay Kaplan.

- Théorie des Modèles et Groupes

Détails :

Orateur / Oratrice : Nick Ramsey
Date : 22 octobre 2019
Horaire : 16h00 - 17h30
Lieu : Sophie Germain salle 1016