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On Kueker's conjecture
Published online by Cambridge University Press: 12 March 2014
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.
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- Copyright © Association for Symbolic Logic 2012
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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