Some remarks on CM-triviality

Ikuo YONEDA

doi:10.2969/jmsj/06120379

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Some remarks on CM-triviality

Ikuo YONEDA

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

JOURNAL FREE ACCESS

2009 Volume 61 Issue 2 Pages 379-391

DOI https://doi.org/10.2969/jmsj/06120379

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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.

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