Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T15:32:22.960Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON NSOP1 IN ONE VARIABLE

Published online by Cambridge University Press:  29 January 2019

NICHOLAS RAMSEY
NICHOLAS RAMSEY*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, LOS ANGELES LOS ANGELES, CA90095, USAE-mail: nickramsey@math.ucla.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We prove that, in order to establish that a theory is NSOP1, it suffices to show that no formula in a single free variable has SOP1.

Keywords

03C45NSOP1one-variable

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019, pp. 388 - 392
Copyright
Copyright © The Association for Symbolic Logic 2019 

References

REFERENCES

Chernikov, A., Theories without the tree property of the second kind. Annals of Pure and Applied Logic, vol. 165 (2014), no. 2, pp. 695–723.10.1016/j.apal.2013.10.002CrossRefGoogle Scholar
Chernikov, A. and Ramsey, N., On model-theoretic tree properties. Journal of Mathematical Logic, vol. 16 (2016), p. 1650009.10.1142/S0219061316500094CrossRefGoogle Scholar
Džamonja, M. and Shelah, S., On ${ \triangleleft ^{\rm{*}}}$-maximality. Annals of Pure and Applied Logic, vol. 125 (2004), no. 1, pp. 119–158.10.1016/j.apal.2003.11.001CrossRefGoogle Scholar
Harrison-Shermoen, G., Independence relations in theories with the tree property, Ph.D. thesis, UC Berkeley, 2014.Google Scholar
Kaplan, I. and Ramsey, N., On Kim-independence. Journal of the European Mathematical Society, to appear.Google Scholar
Lachlan, A. H., A remark on the strict order property. Mathematical Logic Quarterly, vol. 21 (1975), no. 1, pp. 69–70.10.1002/malq.19750210108CrossRefGoogle Scholar