Re: Uncountable sets in CZF?

From: Herman Jurjus (h.jurjus_at_hetnet.nl)
Date: 09/01/04 

Date: Wed, 01 Sep 2004 10:15:02 +0200

David McAnally wrote:

> Herman Jurjus <h.jurjus@hetnet.nl> writes:
>
>
>>Herman Jurjus wrote:
>
>
>>>David McAnally wrote:
>>>
>>>
>>>>A fact which could be considered disturbing is that for any
>>>>transfinite cardinal not cofinal with omega, there exists a model of
>>>>ZFC in which the cardinality of R is the given cardinal.
>>>
>>>
>>>Sorry to bother you once more, but... can you provide a short argument
>>>for this, as well?
>
>
>>Moreover, what's the status of "there exists a transfinite cardinal not
>>cofinal with omega" ?
>
>
> In ZFC, all successor cardinals are regular, so none of them are cofinal
> with omega.

Oh, ok. Apparantly my set theory has become a bit rusty.
What's your definition of 'cofinal with omega'? 

-- 
Cheers,
Herman Jurjus

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