Journal of the Mathematical Society of Japan

Some remarks on CM-triviality

Ikuo YONEDA

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Abstract

We show that any rosy CM-trivial theory has weak canonical bases, and CM-triviality in the real sort is equivalent to CM-triviality with geometric elimination of imaginaries. We also show that CM-triviality is equivalent to the modularity in O-minimal theories with elimination of imaginaries.

Article information

Source
J. Math. Soc. Japan, Volume 61, Number 2 (2009), 379-391.

Dates
First available in Project Euclid: 13 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1242220715

Digital Object Identifier
doi:10.2969/jmsj/06120379

Mathematical Reviews number (MathSciNet)
MR2532894

Zentralblatt MATH identifier
1188.03024

Subjects
Primary: Primary 03C45 03C64: Model theory of ordered structures; o-minimality

Keywords
CM-triviality rosy theories O-minimal theories generic structures geometric elimination of imaginaries

Citation

YONEDA, Ikuo. Some remarks on CM-triviality. J. Math. Soc. Japan 61 (2009), no. 2, 379--391. doi:10.2969/jmsj/06120379. https://projecteuclid.org/euclid.jmsj/1242220715


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