講演者：池上　大祐（ヘルシンキ大学）

題目：Wadge reducibility for the real line

アブストラクト：

In 1968, Wadge introduced Wadge reducibility for the Baire space,
that is an analogue of many-one reducibility in recursion theory. For
two subsets A, B of Baire space, we say A is Wadge reducible to B if
there is a continuous function from the Baire space to itself such
that A = f^{-1} (B). We can introduce Wadge degrees in the same way as
many-one degrees. In the 1970s and 1980s, set theorists in California
developed a beautiful theory of Wadge degree structure under ZF+AD+DC.
On the other hand, we can easily introduce Wadge reducibility on any
topological space as above. In 1998, Woodin claimed that Wadge
reducibility on the real line is totally different from that on the
Baire space. In this talk, we compare them and claim how different
they are. This is joint work with Hisao Tanaka and Philipp Schlicht.