FOM: sharp boundaries/tameness
kanovei at wmwap1.math.uni-wuppertal.de
Thu Feb 14 01:12:12 EST 2002
>Date: Wed, 13 Feb 2002 20:13:32 -0500
>From: Harvey Friedman <friedman at math.ohio-state.edu>
The argument does show that it is not provable in ZF that there is a proper
elementary extension of the field of reals with a predicate for being an
The problem (in ZFC version) was given to me long while ago
by V.A.Uspensky, it appears as an open problem in my paper
(with M.Reeken) in Math Japonica 1996.
What can we say about the niceness of a proper elementary extension in the
case of "tame" expansions of the real field?
There is another problem which I learned from Peano people
also long while ago, which has some connection to this
Problem. Does there exist a Borel nontandard model of PA
whose Scott set is complete, in the sense that for any
standard binary sequence f\in 2^N there is a hyperfinite
binary sequence s of infinite length such that f=s\restriction N.
I guess this one is still open, and both ones are amazingly
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