Re: Review of Mueckenheims book.

In article <r0wAh.12204$d%1.5562@xxxxxxxxxxxxxxxxxxxxxxxxxx> Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx> writes:
*** T. Winter wrote:
However, I think there is an error on p. 88. It is stated that
(translated): "and it is even provable that a well-ordering [of
the reals] can not be defined at all..."
My understanding is that a definable well-order is not inconsistent
with ZF, and there are indeed models were a well-order can be defined.
See: <a href="http://arxiv.org/pdf/math.LO/9812115";>Uri Abraham and
Saharon Shelah, A delta^2_2 well-order of the reals and incompactness
of L(Q^MM)</a>.

There is no need to refer to such a recent paper. V=L already implies
that there is a definable well-ordering of the reals of ridiculously low
complexity. Of course, in reality there is no definable well-ordering of
the reals.

Yes, I know, and I already have discussed that with WM in this newsgroup.
But that was the only quickly available reference I found that contains
a proof.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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