Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T10:02:23.014Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE NUMBER OF COUNTABLE MODELS OF A COUNTABLE NSOP1 THEORY WITHOUT WEIGHT ω

Published online by Cambridge University Press:  02 July 2019

BYUNGHAN KIM
BYUNGHAN KIM*
Affiliation:
DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY 50 YONSEI-RO SEODAEMUN-GU SEOUL 03722, REPUBLIC OF KOREAE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we prove that if a countable non-${\aleph _0}$-categorical NSOP1 theory with nonforking existence has finitely many countable models, then there is a finite tuple whose own preweight is ω. This result is an extension of a theorem of the author on any supersimple theory.

Keywords

03C4503C50NSOP1 theoriessemi-isolationpreweight
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 1168 - 1175
Copyright
Copyright © The Association for Symbolic Logic 2019 

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.)

References

REFERENCES

Chernikov, A. and Ramsey, N., On model-theoretic tree properties. Journal of Mathematical Logic, vol. 16 (2016), no. 2, 1650009.Google Scholar
Dobrowolski, J., Kim, B., and Ramsey, N., Independence over arbitrary sets in NSOP1 theories, preprint.Google Scholar
Herwig, B., Weight ω in stable theories with few types, this Journal, vol. 60 (1995), pp. 353–373.Google Scholar
Kaplan, I. and Ramsey, N., On Kim-independence. Journal of the European Mathematical Society, to appear.Google Scholar
Kaplan, I. and Ramsey, N., Transitivity of Kim-independence, preprint, 2019, arXiv:1901.07026.Google Scholar
Kim, B., On the number of countable models of a countable supersimple theory. Journal of the London Mathematical Society (2), vol. 60 (1999), pp. 641–645.Google Scholar
Kim, B., Simplicity Theory, Oxford University Press, Oxford, 2014.Google Scholar
Lachlan, A. H., On the number of countable models of a countable superstable theory, Logic, Methodology and Philosophy of Science IV (Henkin, L., editor), North-Holland, Amsterdam, 1973, pp. 45–56.Google Scholar
Pillay, A., Countable models of stable theories. Proceedings of the American Mathematical Society, vol. 89 (1983), pp. 666–672.Google Scholar
Shelah, S., Toward classifying unstable theories. Annals of Pure and Applied Logic, vol. 80 (1996), pp. 229–255.Google Scholar