Institute for Mathematical Sciences Programs & Activities
IMSJSPS Joint Workshop in Mathematical Logic and Foundations of Mathematics
(1  5 September 2014)
Organizing Committee · Visitors and Participants · Overview · Activities · Venue
 Chi Tat Chong (National University of Singapore)
 Frank Stephan (National University of Singapore)
 Kazuyuki Tanaka (Tohoku University)
 Yue Yang (National University of Singapore)
This workshop is jointly sponsored by the Japan Society for the Promotion of Science and the National University of Singapore.Â Â 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 prooftheoretic 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 Pideal dichotomy.
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 
10:00am  10:30am 
 Group Photo & Coffee Break  
10:30am  11:15am 
The theory of universally Baire sets in 2^{\omega_1} (PDF) 
11:15am  12:00pm 
Some fixed point theorems and reverse mathematics 
12.00pm  01:30pm 
 Lunch  
01:30pm  02:15pm 
Some remarks on computation on reals (PDF) 
Tuesday, 2 Sep 2014 

09:00am  09:15am 
Registration 
09:15am  10:00am 
A new kind of computability theory on reals (PDF) 
10:00am  10:30am 
 Coffee Break  
10:30am  11:15am 
Coloring on trees and Ramsey's theorem for pairs (PDF) 
11:15am  12:00pm 
Measuring the relative strength of sets of natural numbers (PDF) 
12.00pm  01:30pm 
 Lunch Reception at IMS  
01:30pm  02:15pm 
Lindelöf group with nonLindelöf square and strong negative partition relation (PDF) 
02:15pm  03:00pm 
Nonprincipal ultrafilters, program extraction and higher order reverse mathematics (PDF) 
Wednesday, 3 Sep 2014 

09:00am  09:15am 
Registration 
09:15am  10:00am 
Definability of the ground model and large cardinals (PDF) 
10:00am  10:30am 
 Coffee Break  
10:30am  11:15am 
Termination theorem and Ramsey's theorem (PDF) 
11:15am  12:00pm 
Beyond Peano arithmetic? (PDF) 
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) 
10:00am  10:30am 
 Coffee Break  
10:30am  11:15am 
Randomness in the absence of full induction 
11:15am  12:00pm 
Whitehead problem and ACA_0 (PDF) 
12.00pm  01:30pm 
 Lunch  
01:30pm  02:15pm 
Intuitionistic provability and uniformly provability in RCA (PDF) 
02:15pm  03:00pm 
Some RFtype theorems in reverse mathematics (PDF) 
Friday, 5 Sep 2014 

09:00am  09:15am 
Registration 
09:15am  10:00am 
Weak lowness notions for Kolmogrov complexity (PDF) 
10:00am  10:30am 
 Coffee Break  
10:30am  11:15am 
Expressibility of simple unary generalized quantifier (PDF) 
11:15am  12:00pm 
On exact d.c.e. degrees 
12.00pm  01:30pm 
 Lunch  
01:30pm  02:15pm 
On embedding certain partial orders into the Ppoints under Tukey and RK reducibility (PDF) 
02:15pm  03:00pm 
The role of the axiom DOM in reverse mathematics and its applications to model inductive inference 
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.
Organizing Committee · Visitors and Participants · Overview · Activities · Venue