Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-25T09:27:31.260Z Has data issue: false hasContentIssue false
  • English
  • Français

On Kueker's conjecture

Published online by Cambridge University Press:  12 March 2014

Predrag Tanović
Predrag Tanović*
Affiliation:
Mathematical Institute Sanu, Knez Mihajlova 36, P.P. 367, 11001 Belgrade, Serbia, E-mail: tane@mi.sanu.ac.rs
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that a Kueker theory with infinite dcl(∅) does not have the strict order property and that strongly minimal types are dense: any non-algebraic formula is contained in a strongly minimal type.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1245 - 1256
Copyright
Copyright © Association for Symbolic Logic 2012

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

REFERENCE

[1]Buechler, S., Kueker's conjecture for superstable theories, this Journal, vol. 49 (1984), no. 3, pp. 930–934.Google Scholar
[2]Buechler, S., Vaught's conjecture for superstable theories of finite rank, Annals of Pure and Applied Logic, vol. 155 (2008), no. 3, pp. 135–172.CrossRefGoogle Scholar
[3]Hrushovski, E., Kueker's conjecture for stable theories, this Journal, vol. 54 (1989), no. 1, pp. 207–220.Google Scholar
[4]Newelski, L., ℳ-rank and meager types, Fundamentae Mathematicae, vol. 146 (1995), pp. 121–139.CrossRefGoogle Scholar
[5]Newelski, L., m-normal theories, Fundamentae Mathematicae, vol. 170 (2001), pp. 141–163.CrossRefGoogle Scholar
[6]Newelski, L., Very simple theories without forking, Archive for Mathematical Logic, vol. 42 (2003), no. 6, pp. 601–616.CrossRefGoogle Scholar
[7]Pillay, A. and Tanović, P., Generic stability, regularity, and quasiminimality, Models, logics and higher-dimensional categories, a tribute to the work of Mihály Makkai, CRM Proceedings and Lecture Notes, vol. 53, 2011, pp. 189–211.Google Scholar
[8]Shami, Z., On Kueker simple theories, this Journal, vol. 70 (2005), no. 1, pp. 216–222.Google Scholar
[9]Tanović, P., Minimal first order structures, Slides from the ‘Around Classification Theory’ workshop, Leeds, 2008, http://www.amsta.leeds.ac.uk/-pillay/classification_theory_workshop/tanovic.pdf.Google Scholar
[10]Tanović, P., On constants and the strict order property, Archive for Mathematical Logic, vol. 45 (2006), no. 4, pp. 423–430.CrossRefGoogle Scholar
[11]Tanović, P., Types directed by constants, Annals of Pure and Applied Logic, vol. 161 (2010), no. 7, pp. 944–955.CrossRefGoogle Scholar
[12]Tanović, P., Minimal first order structures, Annals of Pure and Applied Logic, vol. 162 (2011), no. 11, pp. 948–957.CrossRefGoogle Scholar