# Ikuo YonedaNational Institute of Technology Tokuyama College · General education

Ph.D(mathematics)

27
Publications
2,222
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28
Citations
Citations since 2017
6 Research Items
7 Citations
Introduction
Geometric model theory /Current research interests besides model theory: Galois cohomology, Tits buildings/ An external link: https://researchmap.jp/read0104627?lang=en /Pdf files of RIMS Kôkyûroku (Research Institute for Mathematical Sciences at Kyoto Univ.)written by Ikuo Yoneda can be found at https://cir.nii.ac.jp/crid/1410282680092300288
Skills and Expertise
April 2004 - March 2009
Position
• Part-time lecturer
Education
April 1997 - November 2003
University of Tsukuba
Field of study
• model theory

## Publications

Publications (27)
Preprint
Full-text available
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...
Preprint
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...
Article
Full-text available
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...
Article
Full-text available
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
Article
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...
Article
Full-text available
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
Full-text available
Article
Full-text available
Thesis
Thesis (Ph. D. in Mathematics)--University of Tsukuba, (A), no. 3285, 2003.11.30 Includes bibliographical references
Article
Full-text available
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.
Article
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.

Cited By

## Projects

Project (1)
Project
Ehud Hrushovski's new strongly minimal set weakly eliminates imaginaries. Find a new non-trivial strongly minimal set \$D\$ which geometrically eliminates imaginaries but does not weakly eliminate imaginaries, and determine the natural number \$n\$ such that \$D\$ is \$n\$-ample but not \$(n+1)\$-ample.