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Topic: [HM] Faulty Proofs in the History of Mathematics
Replies: 11   Last Post: Oct 30, 2004 8:00 AM

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Roger Cooke

Posts: 242
Registered: 12/3/04
Re: [HM] Faulty Proofs in the History of Mathematics
Posted: Oct 30, 2004 8:00 AM
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Chuck Lindsey's story on the origins of analytic set theory is true.
Aleksandrov (in Luzin's seminar in 1915) was proving that every
uncountable Borel set contains a non-empty perfect subset (so that
the continuum hypothesis is true for Borel sets) when he noticed the
mistake. Suslin noticed that Aleksandrov's proof actually applied
to a larger class of sets than the Borel sets, which he called
A-sets because they were produced by a transfinite inductive process
called the A-operation. (The A was supposed to be for "analytic",
but Aleksandrov said it was for "Aleksandrov".) I mentioned this
story in my 1994 article on "Descriptive set theory and uniqueness
of trigonometric series" in the Archive for History of Exact Sciences.
The basic facts are given in Lebesgue's preface to Luzin's book
"Ensembles analytiques".

Roger Cooke

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