Independence over arbitrary sets in NSOP1 theories

Jan Dobrowolski; Byunghan Kim; Nicholas Ramsey

doi:10.1016/j.apal.2021.103058

Independence over arbitrary sets in NSOP₁ theories

Jan Dobrowolski, Byunghan Kim, Nicholas Ramsey

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Article number	103058
Journal	Annals of Pure and Applied Logic
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2021.103058
Publication status	Published - 2022 Feb

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Logic

Access to Document

10.1016/j.apal.2021.103058

Cite this

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title = "Independence over arbitrary sets in NSOP1 theories",

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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author = "Jan Dobrowolski and Byunghan Kim and Nicholas Ramsey",

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AU - Ramsey, Nicholas

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AB - 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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KW - Kim-dividing

KW - Symmetry

KW - The independence theorem

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