[FOM] Cardinality Beyond Regularity and Choice!

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Tue Dec 15 15:19:10 EST 2009

I would be amazed if gauntt's proof could not be made to work with these 
new objects. And incidentally i don't see why there shouldn't be 
uncountably many of them....

On Dec 15 2009, Zuhair Abdul Ghafoor Al-Johar wrote:

> But the strong version of Extensionality that I wrote shun Quine atoms as 
> well. I am not really sure if those models you are speaking about can be 
> done with Towers of Singletons (recursive Ur-elements {{..}}) i.e. 
> singletons having every member of their transitive closures as singletons 
> also. i.e singletons that are hereditarily singletons. But I doubt it, 
> since we cannot have more than a countable set of these towers. But in 
> case it does, then we should add the axiom that there exist a unique 
> tower of singletons, in this way we also cut the permutations.
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