5 Mar
2009
5 Mar
'09
9:48 a.m.
On 5 Mar 2009, at 15:12, Daniel Fischer wrote:
No, it is an axiom: Cohen showed in 1963 (mentioned in Mendelson, "Introduction to Mathematical Logic") that the continuum hypothesis (CH) is independent of NBG+(AC)+(Axiom of Restriction), where AC is the axiom of choice.
Yes, but the continuum hypothesis is 2^Aleph_0 == Aleph_1, which is quite something different from 2^Aleph_0 == card(R).
Yes, right, card R = 2^Aleph_0, as you said, and Aleph_1 is defined as the smallest cardinal greater than Aleph_0. Hans Aberg