FOM: 53:Free Sets/Reverse Math
Stephen G Simpson
simpson at math.psu.edu
Wed Jul 21 13:59:43 EDT 1999
Harvey Friedman 19 Jul 1999 14:11:48
> This concerns the reverse mathematics of the well known free set
> theorem for omega.
The well known free set theorem? I hadn't heard of this theorem
before. Apparently it says:
For all F:N^k --> N there exists an infinite set A such that for all
x1,...,xk in A, if F(x1,...,xk) is in A then F(x1,...,xk) is among
x1,...,xk.
Harvey, this seems like a nice consequence of Ramsey's theorem, but
what is its motivation? Does it have something to do with the
existence of freely generated subalgebras in a given algebra?
I seem to remember some combinatorial set theory about large cardinals
with properties something like this. Is there a relevant concept
called Jonnson cardinals? I am away from my library and can't easily
look this up.
Harvey, could you perhaps fill in some of this background?
-- Steve
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