# [FOM] Cardinality Beyond Regularity and Choice!

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Mon Dec 14 04:49:01 EST 2009

```The answer is `no'.  See Gauntt's article in the LA 1967 volume.

(This is well-trodden ground, that NFistes in particular have to
know like the back of their hand.   I'm beginning to wonder whether
or not i should write a wikip{\ae}dia/Lonely Planet guide to it.)

> It is well known that Cardinals are defined under the assumptions of
> Choice or Regularity.
>
>The question that present itself is:
>
>Can we define Cardinality for every set in ZF minus Regularity?
>i.e. beyond Choice and Regularity.
>
```

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