[FOM] Countable sets with imprediicative definitions

Monroe Eskew meskew at math.uci.edu
Thu Nov 18 15:54:56 EST 2010

It is consistent that every set has a predicative definition with
parameters.  V=L implies this.


On Thu, Nov 18, 2010 at 2:58 AM, Margaret MacDougall
<Margaret.MacDougall at ed.ac.uk> wrote:
> Can anyone provide examples of countable sets with impredicative
> definitions and apparently no alternative predicative definitions? Just
> to clarify, my intended notion of countable in relation to a set refers
> to the existence of a surjection from the natural numbers (or from the
> natural numbers excluding zero) to that set.
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