
Re: Trichotomy of Cardinals
Posted:
Jul 4, 2014 3:06 PM


William Elliot <marsh@panix.com> writes:
> How is the trichotomy of cardinals equivalent to AxC?
In the form that says that given any two sets A and B, either A and B are equipollent; A and B are not equipollent but A is equipollent to a subset of B; or A and B are not equipollent but B is equipollent to a subset of A.
> Defining the cardinals as done within ZF, as the the initial ordinals, > aren't they well ordered?
Sure.
> Thusly a proof for AxC?
Observing that a class of ordinals is wellordered falls somewhat short of a proof of the axiom of choice.
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus

