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1 Title 表紙 目次 Author(s) Citation 数理解析研究所講究録 (2014), 1888 Issue Date URL Right Type Others Textversion publisher Kyoto University

2 ISSN

3 1964 (2010 ) , , ,383 (2012 )

4 RIMS $K\hat{o}k\gamma\hat{u}roku$ 1888 Model theoretic aspects of the notion of independence and dimension November 18 $\sim$ 20, 2013 edited by Akito Tsuboi April, 2014 Research Institute for Mathematical Sciences Kyoto University, Kyoto, Japan This is a report of research done at the Research Institute for Mathematical Sciences, Kyoto University. The papers contained herein are in fmal form and will not be submitted for publication elsewhere.

5 Model theoretic aspects of the notion of independence and dimension RIMS (Akito Tsuboi) (Koichiro Ikeda) 1. Equivariant definable homotopy extensions $ 1$ (Wakayama $U$.) (Tomohiro Kawakami) $A$ 2. proof of the existence of indiscemible trees without Erd\"os-Rado theorem $ 9$ (Munhehiro Kobayashi) 3. Uncountable $p$-adically closed fields with arithmetic parts satisfying $PA$ $ 17$ (Makoto Yanagawa) 4. Dividing and Forking A Proof of the Equivalence 23 (Akito Tsuboi) 5. Generic structures and model completeness $ 28$ (Hosei $U$.) (Koichiro Ikeda) 6. Resplendent models of -minimal expansions of $0$ RCOF 35 (Yu-ichi Tanaka) 7. Basic properties of definable isomorphisms of quantum 2-tori 44 $T_{q}^{2}(C)$ (Tokai $U$.) (Masanori Itai) 8. INTRODUCTION TO THE CONSTRUCTION OF ADDITIVE INVARIANTS IN $O$-MINIMAL VALUED FIELDS $ -$ 52 U. Pierre et Marie Curie Yimu Yin 9. QUANTIFIER ELIMINATION IN ADELIC STRUCTURES OVER ALGEBRAICALLY CLOSED VALUED FIELDS 57 U. Pierre et Marie Curie Yimu Yin 10. $A$ characterization of $n$ -dependent theories $ -59$ (Kota Takeuchi) 1 1. REGARDING 2-CHAINS WITH 1-SHELL BOUNDARIES IN ROSY THEORIES $ 67$ Yonsei U. Sunyoung Kim $-$ 1

6 12. Some stability condition of atomic types $ -75$ (Waseda $U$.) (Hisatomo Maesono) 13. Graph axiom and model companion $ 83$ (Takehiro Naito) 14. The strong continuity in weakly -minimal structures $ -87$ $0$ (Hiroshi Tanaka) $(Kin]\dot{\mathfrak{a}} U.)$ 15. Elementary equivalence of rational function fields of many variables $ -93$ (Int. U. Kagoshima) (Kenji Fukuzaki) $-$ li. $1$

7 K\^oky\^uroku $K\hat{0}ky\hat{u}\iota \mathfrak{v}ku$ RIMS was started in 1964 as the proceedings of symposia, colloquia and workshops supported by RIMS, the Research Institute for Mathematical Sciences, Kyoto University It was the next year of the establishment of $RnIS$ as one of the nationwide Cooperative Research Centers, the preceding system of the current Joint UsagelResearch Centers that started in For half a century since then, about 50 to 60 volumes have been issued each year, and the 1, $800th$ volume was issued in The volumes of from $K\hat{o}br\hat{u}roku$ the lst through the 1,$840th$ containing enormous 26,808 articles and 317,199 pages, not only deliver the latest research activities in mathematics and mathematical sciences but also constitute valuable and incomparable collections of articles that pass down history of progress of mathematics and mathematical science in Japan. $K\hat{0}ky\^{u}\iota \mathfrak{v}ku$ Articles in are available on the websites of RIMS and Kyoto University Research Information Repository They are very frequently accessed on the internet, with a total of as many as 1,254,383 accesses in The authors choose the languages to write articles, and many are written in Japanese, which is one of the characteristics of $K\hat{0}$]$qr\hat{u}roku$. As a result, $K\hat{o}b\hat{u}xoku$ is regarded as a significant and important literature which allows easy access to the latest speciahzed knowledge in the large fields of mathematics and mathematical sciences written in native language $for$ Japanese readers, while more and more research papers are being written in English in oeoent years. We are deeply grateful to many of those who have participated in cooperative research activities of RIMS and greatly developed K6ky\^uroku. We heartily ask $f0r$ your continuous participation in research activities at RIMS as a Joint Usage Research Center and your warm support and cooperation $f0r$ the fruitful development of $K\hat{o}$]$g^{r}\hat{u}\iota oku.$