Independence over arbitrary sets in NSOP1 theories

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Annals of Pure and Applied Logic 173 (2):103058 (2022)
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Abstract

We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types

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10.1016/j.apal.2021.103058

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Nicholas Ramsey
University of California, Los Angeles

Citations of this work

Nsop-Like Independence in Aecats.Mark Kamsma - forthcoming - Journal of Symbolic Logic:1-34.
On Rank Not Only in Nsop Theories.Jan Dobrowolski & Daniel Max Hoffmann - forthcoming - Journal of Symbolic Logic:1-34.
Three Surprising Instances of Dividing.Gabriel Conant & Alex Kruckman - forthcoming - Journal of Symbolic Logic:1-20.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
On model-theoretic tree properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Generic expansion and Skolemization in NSOP 1 theories.Alex Kruckman & Nicholas Ramsey - 2018 - Annals of Pure and Applied Logic 169 (8):755-774.
Generic expansions by a reduct.Christian D’Elbée - 2021 - Journal of Mathematical Logic 21 (3):2150016.

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