[logic-ml] Talk by Dieter Spreen (April 4, Fukuoka)

[Akitoshi Kawamura]

皆様

九州大学の河村です。ディーター・シュプレーン先生（ジーゲン大）の講演を
以下のように開催いたしますので、お近くの方はどうぞお越しください。
http://www.i.kyushu-u.ac.jp/~kawamura/seminar/H300404.html

日時　April 4, 2018, Wednesday, 15:30–
場所　Room 314, Ito Campus West Building II, Kyushu University
(九州大学伊都キャンパスウエスト二号館314第四講義室)

The continuity problem in computability theory
Dieter Spreen (University of Siegen)

After the discovery of the paradoxes in Cantor's set theory, mathematics
was in a deep foundational crisis. Various suggestions of how to get out
of this situation have been made. The more radical among them required
that it is no longer sufficient to derive the existence of an object by
indirect reasoning, but to present a concrete construction of the object
under consideration. Here, the problem is what is meant by a
construction. Markov replaced "construction" by "algorithm": only those
objects should be considered that are generated by an algorithm.

This should in particular be true for functions. So, in the Markov
school, also known as Russian Constructivism, a function is given by an
algorithm that takes as input an algorithm generating the object the
function is applied to, and delivers as output an algorithm generating
the function value.

This is a rather restrictive concept. When dealing with functions on the
real numbers, e.g., we are interested in their computability, but we do
not want to restrict the function to only computable real numbers as
arguments. Such functions turn out to be computable, if they are
continuous with a computable modulus of continuity.

In several cases it turned out that Markov computable functions can be
extended to computable functions in the sense just mentioned. However,
it is known that this is not true in general. The problem in which
situations Markov computable functions can be extended to computable
functions is known as the continuity problem. It will be discussed in
this talk.

皆様のご参加をお待ちしております。

-- 
河村彰星
九州大学システム情報科学研究院情報学部門
〒819-0395　福岡市西区元岡744
092-802-3806
kawamura at inf.kyushu-u.ac.jp