TITLE: Continuum Hypothesis
QUESTION [15 upvotes]: I am new here, so forgive me if this question does not satisfy the protocols of the site. 
I know there are so many equivalents to the AC (axiom of choice) and there are books that lists this equivalent forms of AC. 
But how can I find equivalent forms of the continuum hypothesis ?
Specially I am interested in Algebraic equivalent form. 
What references do we have in the literature !? 
Thanks in Advance.

REPLY [2 votes]: A very simple algebraic statement equivalent to CH is the assertion that the Baer-Specker group $\mathbb{Z}^{\omega}$ is almost free, i.e. all its subgroups of cardinality less than $\mid \mathbb{Z}^{\omega} \mid$ are free. (This is somewhat unsatisfactory in that almost freenees refers to cardinality.)