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Topic:
Trichotomy of Cardinals
Replies:
10
Last Post:
Jul 4, 2014 5:33 PM




Re: Trichotomy of Cardinals
Posted:
Jul 4, 2014 5:20 PM


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



