Ikuo Yoneda

National Institute of Technology Tokuyama College · General education

The smallest algebraically closed set which appears in Poizat's original definition for WEI coincides with algebraic closure of finite real tuple which appears in Pillay's alternative definition for WEI. 1. Two definitions for WEI Let M be a sufficiently saturated model of T .ā,b,c,. .. denote finite tuples in M and a, b, c,. .. denote elements of...

We give an explicit proof of Fact 2.2.2 in [CF]. 1. The characterization of WEI Let M be a sufficiently saturated model of T .ā,b,c,. .. denote finite tuples in M and a, b, c,. .. denote elements of M. L(ā) denotes the set of L-formulas with parameterā. For ϕ(x,ā) ∈ L(ā), ϕ(x,ā) M := {m ⊂ M : M |= ϕ(m,ā)}. We work in M eq := {ā/E :ā/E is the E-clas...

We give an explicit proof of Fact 2.2.2 in [CF]

We give an explicit proof of Fact 2.2.2 in [CF].

We give an explicit proof of Fact 2.2.2 in [CF]

We begin with basic theory on valued fields based on the book ''Valued fields'' written by A.J.Engeler, A.Prestel, published in 2005, Springer Monographs in Mathematics. And then, we introduce two results on quantifier elimination of henselian valued fields having nice languages. Finally we present some results on NTP_2 related to henselian valued...

In rosy theories we introduce a geometric notion of independence, strong non-3-ampleness, and we show that strong non-3-ampleness implies non-3-ampleness, and non-2-ampleness(=CM-triviality) implies strong non-3-ampleness

We present results of our paper “Some remarks on CM-triviality” [J. Math. Soc. Japan 61, No. 2, 379–391 (2009; Zbl 1188.03024)] which show that any rosy CM-trivial theory has weak canonical bases and any CM-trivial o-minimal theory having elimination of imaginaries is modular. In the last section we show that one-basedness is equivalent to weak one...

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.

Thesis (Ph. D. in Mathematics)--University of Tsukuba, (A), no. 3285, 2003.11.30 Includes bibliographical references

Continuing work of Baldwin and Shi (Ann. Pure Appl. Logic 79 (1996) 1), we study non-ω-saturated generic structures of the ab initio Hrushovski construction with amalgamation over closed sets. We show that they are CM-trivial with weak elimination of imaginaries. Our main tool is a new characterization of non-forking in these theories.

 We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable CM-trivial with weak elimination of imaginaries.