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Independence over arbitrary sets in NSOP1 theories
Annals of Pure and Applied Logic 173 (2):103058 (2022)
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 typesAuthor's Profile
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Citations of this work
Three Surprising Instances of Dividing.Gabriel Conant & Alex Kruckman - forthcoming - Journal of Symbolic Logic:1-20.
On Rank Not Only in Nsop $_1$ Theories.Jan Dobrowolski & Daniel Max Hoffmann - 2024 - Journal of Symbolic Logic 89 (4):1669-1702.
Generic multiplicative endomorphism of a field.Christian D'Elbée - 2025 - Annals of Pure and Applied Logic 176 (4):103554.
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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