On 23 Jun., 15:25, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > WM <mueck...@rz.fh-augsburg.de> writes: > > Therefore, there is not every subset of an infinite set. > > What on Earth does this mean?
It is Fraenkels text. I thought that you could understand German?
In 1928 Fraenkel had realized Skolems proof (if a first-order-logic theory is consistent, then it has a countable model). In order to circumvent this problem, Fraenkel (and the later interpreters of the axiom of power set) must keep open the possibility that only countably many subsets of omega may exist. Hence, not all subsets exist "automatically".
