and Gaisi Takeuti's 77th Birthday

The *Symposium on Mathematical Logic* is a series of meetings
on mathematical logic in a broad sense, supported by
the Division of Mathematical Logic of the Mathematical Society of Japan.
This year's symposium was held in honor of
50 years of Takeuti's Conjecture and Gaisi Takeuti's 77th birthday
(the Age of Joy, in Japanese tradition)
at Centennial Hall (Shindai-Kaikan) of
Kobe University.
The symposium was divided into two sections, namely

- 50 Years of Takeuti's Conjecture
- Recent Developments in Mathematical Logic

**Organization**

- Program Committee: T. Arai (Kobe), J. Brendle (Kobe), Y. Kakuda (Kobe, co-chair), M. Okada (Keio), H. Ono (JAIST, co-chair)
- Local Organizing Committee: M. Banbara (Kobe), M. Kikuchi (Kobe, chair), I. Nagasaka (Kobe), A. Suzuki (Kobe), S. Yatabe (Kobe)

**Invited Speakers**

- One Hour Talks: S. Buss (San Diego), P. Hajek (Prague), J. Krajicek (Prague), G. Mints (Stanford), W. Pohlers (Muenster), G. Takeuti, S. Titani (Chubu Univ), M. Yasugi (Kyoto Sangyo Univ), M. Yasumoto (Nagoya)
- Panel Discussion: T. Arai (Kobe), G. Mints (Stanford), M. Okada (Keio, moderator), W. Pohlers (Muenster), G. Takeuti, M. Yasugi (Kyoto Sangyo Univ)

**Banquet**

The banquet of the symposium, in celebration of Gaisi Takeuti's 77th birthday, was held in the evening of December 17 at a restraurant SOSHUEN. (In Japanese tradition, 77 years old is called "the Age of Joy", since the Chinese characters for "77" bear a resemblance to the Chinese character for "Joy".)

**Sponsors**

- Inoue Foundation for Science
- JSPS Grants-in-Aid for Scientific Research

The list of the participants of the symposium is here.

**Photos**

- Inbited speakers and Panel Discussion
- Banquet
- Photo of all the participants is here.

**December 17 (Wed), 2003**

- 09.00- (registration)
- 09.20-09.30 [Opening (Ono)]
- 09.30-11.40 [Invited Talks 1, Chair: T. Arai (Kobe)]
**G. Mints**(Stanford),**W. Pohlers**(Muenster) - (12.10-13.00 Business Meeting of ASL committee on Logic in East Asia)
- 13.30-15.30 [Contributed Talks 1]
- 16.00-17.00 [Invited Talks 2, Chair: M. Okada (Keio)]
**G. Takeuti** - 19.00- (banquet)

- 09.30-11.40 [Invited Talks 3, Chair: S. Titani (Chubu)]
**M. Yasumoto**(Nagoya),**M. Yasugi**(Kyoto Sangyo Univ) - 13.30-15.00 [Contributed Talks 2]
- 15.30-17.00 [Panel Discussion]
**50 Years of Takeuti's Conjecture**

[T. Arai (Kobe), G. Mints (Stanford), M. Okada (Keio, moderator), W. Pohlers (Muenster), G. Takeuti, M. Yasugi (Kyoto)]

**December 19 (Fri), 2003**

- 09.30-11.40 [Invited Talks 4, Chair: M. Ozawa (Tohoku)]
**J. Krajicek**(Prague),**S. Buss**(San Diego) - 13.30-14.30 [Contributed Talks 3]
- 14.50-17.00 [Invited Talks 5, Chair: H. Ono (JAIST)]
**P. Hajek**(Prague),**S. Titani**(Chubu) - 17.00 [Closing]

**December 17 (Wed), 2003**

- 09.30-10.30
**G. Mints**A proof of topological completeness for S4C in Cantor space (joint paper with Ting Zhang) - 10.40-11.40
**W. Pohlers**Fifty years of fundamental conjecture: A personal account - 16.00-17.00
**G. Takeuti**P and NP

- 09.30-10.30
**M. Yasumoto**Separations of first and second order theories in bounded arithmetic - 10.40-11.40
**M. Yasugi**Computability problems on the continuum

**December 19 (Fri), 2003**

- 09.30-10.30
**J. Krajicek**Hardness assumptions in the foundations of theoretical computer science - 10.40-11.40
**S. Buss**Bounded Arithmetic and Bounded Depth Propositional Systems - 14.50-15.50
**P. Hajek**Mathematical fuzzy logic and set theory developed in it - 16.00-17.00
**S. Titani**Quantum Set Theory

**December 17 (Wed), 2003**

[Session 1A, Chair: M. Kumabe (U. of the Air)]

- 13.30-14.00
**N.-Y. Suzuki and M. Kaneko**Epistemic Logic of Shallow Depths arising from Game Theoretical Decision Making - 14.00-14.30
**M. Kanazawa**Computing Interpolants in Implicational Logic - 14.30-15.00
**H. Towsner**A Realizability Interpretation of Classical Analysis - 15.00-15.30
**C.T. Chong**Recursion Theory from the Proof-theoretic Point of View

- 13.30-14.00
**J. Moore**Set Mapping Reflection - 14.00-14.30
**T. Yorioka**The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap - 14.30-15.00
**D. Aspero**Forcing notions in inner models - 15.00-15.30
**K. Eda**Transparent explanation of ultra-discrete limits by non-standard analysis

**December 18 (Thu), 2003**

[Session 2A, Chair: Y. Andou (Hosei)]

- 13.30-14.00
**S. Kuroda**Applicative theories and boolean circuit complexity classes - 14.00-14.30
**K. Terui**Boolean circuits and proof nets - 14.30-15.00
**S. Cook and T. Morioka**Quantified Propositional Calculus and ALOGTIME

- 13.30-14.00
**B. Koening and Y. Yoshinobu**Game closed posets and forcing axioms - 14.00-14.30
**K. Sato**Stalker theory - 14.30-15.00
**T. Murata**Introduction to "The Problem of Continuity"

**December 19 (Fri), 2003**

[Session 3A, Chair: K. Tanaka (Tohoku)]

- 13.30-14.00
**O. Takaki**Primitive recursive analogues of several regular cardinals up to the least Mahlo cardinal - 14.00-14.30
**N. Sakamoto**On the strength of the Jordan curve theorem

- 13.30-14.00
**M. Shimoda**Sheaf model and fuzzy set theory - 14.00-14.30
**T. Suzuki**Forcing complexity: degree of randomness shown by minimum sizes of forcing conditions

For further information, please contact:

- Toshiyasu Arai

Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan

E-mail: arai@kurt.scitec.kobe-u.ac.jp, Tel/Fax: 078-803-6245

Last Modified December 24, 2003