FOM: Does Mathematics Need New Axioms?
kanovei at wmfiz4.math.uni-wuppertal.de
Thu May 11 11:58:24 EDT 2000
>Date: Wed, 10 May 2000 10:40:23 -0400
>From: Harvey Friedman <friedman at math.ohio-state.edu>
>Does Mathematics Need New Axioms?
Mathematics does not need new axioms because it cannot
need, it is particular mathematicians who need (or who
do not need) new axioms, and the matter is how many of
them need and do they need one and the same and is it
at least compatible with each other or those who need
would better keep the status quo than join the other boat.
It would perhaps happen now that quite a lot of set
theorists (optimistically > than half) would vote to
accept some kind of a "Woodin-cardinal" axiom.
But this is not really new. AD and PD were not less
popular in 70s but look now at papers in descriptive set
theory published in 1999, how much of determinacy
stuff is there ? Scattered.
What happened with determinacy then ?
Apparently the topic has just exhausted itself.
How about ZFC ? Still there. Why ? Strange.
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