
Re: Trichotomy of Cardinals
Posted:
Jul 4, 2014 5:25 PM


"Ross A. Finlayson" <ross.finlayson@gmail.com> writes:
> On 7/4/2014 12:06 PM, Aatu Koskensilta wrote: >> 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. >> > > 2 <> 3
This is no doubt a pertinent observation, if somewhat obscure.
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus

