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From: Robert E. Beaudoin on 29 May 2010 18:12
On 05/29/10 03:41, Rupert wrote:
> I think I might have asked this before.
>
> In his article "The Continuum Hypothesis, Part I" Hugh Woodin writes
>
> "In 1978 Martin succeeded in proving the determinacy of all boldface
> Sigma^1_2 sets using essentially the strongest large-cardinal
> hypothesis known at the time. Finally in 1983 I proved the determinacy
> of all projective sets using large cardinal axioms in a natural
> hierarchy which begins with the large cardinal axiom Martin used to
> establish the determinacy of all boldface Sigma^1_2 sets."
>
> http://www.ams.org/notices/200106/fea-woodin.pdf
>
> I am interested in finding out more about what this "natural
> hierarchy" was. If anyone could direct me to the original papers that
> would be great.

I expect Woodin was simply referring to the hierarchical ordering of
large cardinals by consistency strength, or at least that part of it
above a measurable cardinal (and perhaps below a Woodin cardinal, or
maybe below a supercompact). I can't point you to original papers, but
Aki Kanamori's book _The Higher Infinite_ is a good reference (and may
have some pointers back to the original literature).

Hope that helps,
Robert E. Beaudoin
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