2009Journal of the Mathematical Society of JapanOpen access

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.

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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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Available 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.

Key concepts: Triviality, sort, Mathematics, Modularity (biology), Pure mathematics, Theoretical physics, Physics, Arithmetic

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