evert@botter.UUCP (Evert Wattel) (11/26/85)
We here in the Topology section, (and especially K.P. Hart )
have a problem concerning Martin's theorem which states that every
Borel game is determined.
The original paper of 1975 in the Annals of Mathematics delivers a
proof for this theorem, but only for the case of a well established
finite number of steps in the Borel hierarchy, and claims that
the general case can be handled in a similar way.
However, nobody in our neighborhood has ever seen this similar case
carefully worked out in print, or in such a form that the details
can be checked.
There are some rumors in Prague lately that the general case could
very well be wrong.
If somebody on the net is close to a group which works in descriptive
set theory, would he please try to get an answer to the very question
if either there is a "full proof" or there is a serious flaw in the
theorem.
Many thanks in advance,
K.P. Hart & Evert Wattel
Dept of Math and computer science,
Free university, Amsterdam
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