Sendai Logic School 2015
■Conference Venue
10 March (Tuesday), 2015
Kawai Hall, Tohoku University（Mathematical Institute）
[日本語/English]
■Speakers
Stanley Wainer (Leeds)
NingNing Peng (Singapore)
Keita Yokoyama (JAIST)
■Program
March 10th 
TIME 
Speaker 
14:00  14:30 
NingNing Peng 
14:45  15:45 
Keita Yokoyama 
16:00  17:00 
Stanley Wainer 
■Abstracts
NingNing Peng

Title: A generalization of LiuTanaka theorem
Abstract: In 2007, Liu and Tanaka show that for any uniform binary ANDOR tree on the assignments that are independently distributed (ID),
the distributional complexity is achieved only if the assignments are also identically distributed (IID).
We generalize LiuTanaka's result to uniform levelbylevel $k$brabching ANDOR tree.
The technique is different from available proofs. One part of our proof is by generalize SuzukiNiida's "fundamental relationships between costs and probabilities".
Another part of our proof is by analyse the algorithms.

Keita Yokoyama

Title: Several questions on the restricted versions of Ramsey's theorem
Abstract: In the field of reverse mathematics, so many variations of Ramsey's
theorem are studied, e.g., stable Ramsey theorem, transitive Ramsey
theorem, Rainbow Ramsey theorem, thin set theorem, pseudo Ramsey
theorem, etc. Although many important works are done in this area,
there still remain a lot of interesting questions. In this talk, I
will try to classify some of these, and show many questions which
should be solved.

Stan Wainer

Title: A miniaturized predicativity
Abstract: This talk attempts to characterize those recursive functions which are "predictably terminating" according to a finitistic point of view.
The basis of the work is Leivant's (1995) theory of ramified induction over N, which has elementary recursive strength.
It has been redeveloped and extended in various ways by many people.
Eg. Spoors & W. (2012) built a hierarchy of ramified "inputoutput" theories whose strengths correspond to the levels of the Grzegorczyk hierarchy.
Here, a further extension of this hierarchy is developed, with one additional input level on top (level omega).
The underlying logic is an autonomously generated infinitary calculus with arbitrary finitelymany stratification levels of numerical inputs and a ramified Repetition Rule.
The autonomous control on allowable ordinals is based on a weak (finitistic) notion of "pointwise transfinite induction".
It turns out that the ordinal of this theory is then Gamma0;
the provably computable functions are those which are resourcebounded by the slow growing hierarchy;
and these are the functions elementary recursive in the Ackermann function.

■Links
[sendai logic homepage]
https://sites.google.com/site/sendailogichomepage/
[JSPSNUS Joint Workshop in Mathematical Logic and Foundations of Mathematics]
http://www.math.tohoku.ac.jp/~tanaka/kanazawa2015
[Sendai Logic School]
[2013]http://sendailogic.math.tohoku.ac.jp/SLS/
[2014]http://www.sendailogic.com/SLS2014/
