FOM: Does Mathematics Need New Axioms?

[Kanovei]

>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. 

Vladimir Kanovei