Hostname: page-component-68c7f8b79f-4ct9c Total loading time: 0 Render date: 2026-01-16T23:25:45.153Z Has data issue: false hasContentIssue false
  • English
  • Français

EXISTENCE IN NSOP1 THEORIES

Part of: Model theory

Published online by Cambridge University Press:  13 October 2025

BYUNGHAN KIM ,
JOONHEE KIM  and
HYOYOON LEE
BYUNGHAN KIM
Affiliation:
DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY REPUBLIC OF KOREA E-mail: bkim@yonsei.ac.kr
JOONHEE KIM*
Affiliation:
SCHOOL OF MATHEMATICS KOREA INSTITUTE FOR ADVANCED STUDY REPUBLIC OF KOREA
HYOYOON LEE
Affiliation:
DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY REPUBLIC OF KOREA E-mail: bkim@yonsei.ac.kr DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY REPUBLIC OF KOREA CENTER FOR NANO MATERIALS G-LAMP, SOGANG UNIVERSITY REPUBLIC OF KOREA E-mail: hyoyoonlee@sogang.ac.kr
*
E-mail: kimjoonhee@kias.re.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that Kim-forking satisfies existence in all NSOP1 theories.

Keywords

NSOP1 theoriesKim-forkingexistencetree indiscernibility

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C50: Models with special properties (saturated, rigid, etc.)

Information

Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 15
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

This article was originally published with incorrect author affiliations. The errors have been corrected and the online HTML and PDF versions updated.

References

Chernikov, A., Kim, B., and Ramsey, N., Transitivity, lowness, and ranks in NSOP ${}_1$ theories. Journal of Symbolic Logic , vol. 88 (2023), pp. 919–946.CrossRefGoogle Scholar
Chernikov, A. and Ramsey, N., On model-theoretic tree properties . Journal of Mathematical Logic , vol. 16 (2016), no. 2, p. 1650009.CrossRefGoogle Scholar
Dobrowolski, J., Kim, B., and Ramsey, N., Independence over arbitrary sets in NSOP ${}_1$ theories. Annals of Pure and Applied Logic , vol. 173 (2022), p. 103058.CrossRefGoogle Scholar
Kaplan, I. and Ramsey, N., On Kim-independence . Journal of the European Mathematical Society , vol. 22 (2020), pp. 1423–1474.CrossRefGoogle Scholar
Kaplan, I. and Ramsey, N., Transitivity of Kim-independence . Advances in Mathematics , vol. 379 (2021), p. 107573.CrossRefGoogle Scholar
Kim, B., Simplicity Theory , Oxford University Press, Oxford, 2013.CrossRefGoogle Scholar
Kim, B., Weak canonical bases in NSOP ${}_1$ theories. Journal of Symbolic Logic , vol. 86 (2021), pp. 1259–1281.CrossRefGoogle Scholar
Kim, B., Kim, H.-J., and Scow, L., Tree indiscernibilities, revisited . Archive for Mathematical Logic , vol. 53 (2014), pp. 211–232.CrossRefGoogle Scholar
Mutchnik, S., An NSOP ${}_1$ theory without the existence axiom, preprint, 2024. https://arxiv.org/abs/2407.13082Google Scholar
Shelah, S., Simple unstable theories . Annals of Mathematical Logic , vol. 19 (1980), pp. 177–203.CrossRefGoogle Scholar
Shelah, S., Classification Theory and the Number of Nonisomorphic Models , North-Holland, Amsterdam, 1990, revised.Google Scholar