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IMS-JSPS Joint Workshop in Mathematical Logic and Foundations of Mathematics
(1 - 5 September 2014)

 

Organizing Committee · Visitors and Participants · Overview · Activities · Venue

 

 Organizing Committee



 Visitors and Participants

 

 

 Overview

 

This workshop is jointly sponsored by the Japan Society for the Promotion of Science and the National University of Singapore.   In recent years, the interaction among researchers in East Asia, particularly in Japan, China and Singapore in foundations and other areas of mathematical logic has increased significantly. Two successful workshops in computability theory (recursion theory) and the foundations of mathematics were held in the city of Tokyo in 2013 and 2014. This workshop is intended to provide a venue for continued interaction and to serve as an opportunity to explore new research collaborations in three broad areas of common interest: reverse mathematics (involving both standard and nonstandard models of arithmetic), algorithmic randomness (in both classical and higher setting), and set theory (particularly cardinal characters of the continuum).

The central theme of reverse mathematics is to investigate the proof-theoretic strength of a mathematical theorem. Its history goes back to Hilbert's program on the foundations of mathematics, and techniques in recursion theory have been successfully introduced to investigate problems in reverse mathematics. As examples, there have been major developments in the study of combinatorial principles related to Ramsey's theorem for pairs, resolving several outstanding problems in reverse mathematics. The techniques involved both standard and nonstandard models of arithmetic.

Randomness is a mathematical concept that spans over a broad class of mathematical objects from finite words to transfinite cardinals. Classical probability theory deals with distributions of randomly chosen objects; however, it does not formulate or even allow for a definition of an individual random object. There is an enduring appeal to the intuitive notion of a real number or of an infinite binary sequence which looks as chosen at random. This intuitive notion can be made more precise when it is interpreted within an effective framework: no effective test detects any regularity in the real number. An elegant and useful characterisation of the randomness of an infinite binary sequence R is given by the algorithmic incompressibility of its finite initial segments: A infinite binary sequence R is random if for almost every finite initial segment I of R there does not exist any description of I (for example, by means of a computer program) which is essentially shorter than the initial segment itself. This approach permits one to calibrate degrees of randomness, characterise applications of randomness and prove preservation of randomness across type, such as between real numbers on the line and sample paths in Brownian motion. In addition, ideas and techniques from effective descriptive set theory may be introduced to investigate randomness from the point of view of second order definability.

The broad area of set theory of the reals has seen a lot of recent activity by researchers in Japan and in Singapore. One topic of interest within this area is cardinal characteristics of the continuum, which capture certain combinatorial features of the set of real numbers. There have a number of recent advances in this field, most notably the proof by Malliaris and Shelah that p = t. Closely related to this is the study of the descriptive complexity of certain maximal families of sets of reals, such as almost disjoint families and ultrafilters. Recent work on this has been done by both sides. Another broad area of mutual interest is the study of limitations of forcing axioms such as PFA and MM and their consequences such as the P-ideal dichotomy.


 Activities

 

Monday, 1 Sep 2014

08:50am - 09:10am

Registration

09:10am - 09:15am

Opening Remarks

Chi Tat Chong, National University of Singapore

09:15am - 10:00am

Variants of infinite games and their strength
Kazuyuki Tanaka, Tohoku University, Japan

10:00am - 10:30am

--- Group Photo & Coffee Break ---

10:30am - 11:15am

The theory of universally Baire sets in 2^{\omega_1} (PDF)
Daisuke Ikegami, Kobe University, Japan

11:15am - 12:00pm

Some fixed point theorems and reverse mathematics
Takeshi Yamazaki, Tohoku University, Japan

12.00pm - 01:30pm

--- Lunch ---

01:30pm - 02:15pm

Some remarks on computation on reals (PDF)
Yue Yang, National University of Singapore

Tuesday, 2 Sep 2014

09:00am - 09:15am

Registration

09:15am - 10:00am

A new kind of computability theory on reals (PDF)
Longyun Ding, Nankai University, China

10:00am - 10:30am

--- Coffee Break ---

10:30am - 11:15am

Coloring on trees and Ramsey's theorem for pairs (PDF)
Wei Li, University of Vienna, Austria

11:15am - 12:00pm

Measuring the relative strength of sets of natural numbers (PDF)
Keng Meng Ng, Nanyang Technological University

12.00pm - 01:30pm

--- Lunch Reception at IMS ---

01:30pm - 02:15pm

Lindelöf group with non-Lindelöf square and strong negative partition relation (PDF)
Yinhe Peng, Chinese Academy of Sciences, China

02:15pm - 03:00pm

Non-principal ultrafilters, program extraction and higher order reverse mathematics (PDF)
Alexander Kreutzer, National University of Singapore

Wednesday, 3 Sep 2014

09:00am - 09:15am

Registration

09:15am - 10:00am

Definability of the ground model and large cardinals (PDF)
Toshimichi Usuba, Kobe University, Japan

10:00am - 10:30am

--- Coffee Break ---

10:30am - 11:15am

Termination theorem and Ramsey's theorem (PDF)
Keita Yokoyama, Japan Advanced Institute of Science and Technology, Japan

11:15am - 12:00pm

Beyond Peano arithmetic? (PDF)
Tin Lok Wong, University of Vienna, Austria

12.00pm - 01:30pm

--- Lunch ---

Thursday, 4 Sep 2014

09:00am - 09:15am

Registration

09:15am - 10:00am

Some properties of probability theory in reverse mathematics (PDF)
Ningning Peng, National University of Singapore

10:00am - 10:30am

--- Coffee Break ---

10:30am - 11:15am

Randomness in the absence of full induction
Chi Tat Chong, National University of Singapore

11:15am - 12:00pm

Whitehead problem and ACA_0 (PDF)
Sen Yang, Inner Mongolia University, China

12.00pm - 01:30pm

--- Lunch ---

01:30pm - 02:15pm

Intuitionistic provability and uniformly provability in RCA (PDF)
Makoto Fujiwara, Tohoku University, Japan

02:15pm - 03:00pm

Some RF-type theorems in reverse mathematics (PDF)
Shota Murakami, Tohoku University, Japan

Friday, 5 Sep 2014

09:00am - 09:15am

Registration

09:15am - 10:00am

Weak lowness notions for Kolmogrov complexity (PDF)
Ian Herbert, National University of Singapore

10:00am - 10:30am

--- Coffee Break ---

10:30am - 11:15am

Expressibility of simple unary generalized quantifier (PDF)
Shohei Okisaka, Tohoku University, Japan

11:15am - 12:00pm

On exact d.c.e. degrees
Guohua Wu, Nanyang Technological University

12.00pm - 01:30pm

--- Lunch ---

01:30pm - 02:15pm

On embedding certain partial orders into the P-points under Tukey and RK reducibility (PDF)
Dilip Raghavan, National University of Singapore

02:15pm - 03:00pm

The role of the axiom DOM in reverse mathematics and its applications to model inductive inference
Frank Stephan, National University of Singapore

 

Students and researchers who are interested in attending these activities are requested to complete the online registration form.

The following do not need to register:

  • Those invited to participate.


 Venue

 

 

Organizing Committee · Visitors and Participants · Overview · Activities · Venue

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