Transitivity, Lowness, And Ranks In Nsop Theories

Artem Chernikov; Byunghan Kim; Nicholas Ramsey

doi:10.1017/jsl.2023.36

Transitivity, Lowness, And Ranks In Nsop Theories

Artem Chernikov, Byunghan Kim, Nicholas Ramsey

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We develop the theory of Kim-independence in the context of NSOP theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP theories.

Original language	English
Pages (from-to)	919-946
Number of pages	28
Journal	Journal of Symbolic Logic
Volume	88
Issue number	3
DOIs	https://doi.org/10.1017/jsl.2023.36
Publication status	Published - 2023 Sept 9

Bibliographical note

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© 2023 The Author(s). Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

All Science Journal Classification (ASJC) codes

Philosophy
Logic

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10.1017/jsl.2023.36

Cite this

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AB - We develop the theory of Kim-independence in the context of NSOP theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP theories.

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KW - neostability theory

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Transitivity, Lowness, And Ranks In Nsop Theories

Abstract

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