Talk:Urelement

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[edit] category theory and urelements

Is there, or could there be created, a categorical definition of urelement?Rich 01:38, 9 September 2006 (UTC)

Interesting. I'm not familiar with any real work done on that matter, but I can offer my thoughts. One trouble with a categorical definition of urelements is that if morphisms are taken to be functions, how would one define functions on something which is not a set? One possibility would be to not define them, and then maybe call urelements those things on which there are only identity morphisms, but then you would lose some crucial properties of the category of sets, e.g., the existance of terminal objects. Another possibility is to treat urelements as distinct empty sets, and then you can define urelements as objects isomorphic to 0 but not identical with 0. Just my uninformed suggestions. Phill 11:11, 8 July 2007 (UTC)

[edit] Prefix Ur

Is there any reason for this prefix ur-? Albmont 20:28, 5 February 2007 (UTC)

Mathworld reports:

"Ur" is a German prefix which is difficult to translate literally, but has a meaning close to "primeval."

— Arthur Rubin | (talk) 20:47, 5 February 2007 (UTC)

Thanks! Maybe this should go into the text? I had seen this prefix before in GURPS Uplift (ur-species), but I didn't think it came from a real world language (many expressions in the Uplift Universe come from alien conlangs). Albmont 13:25, 6 February 2007 (UTC)

[edit] NFU

Hello, I'm french and read this article for the french's one I have written.

I have a poor level in english, excuse me.

I don't understand this sentence :

"NFU is consistent with the axiom of choice whereas NF disproves it" What means?

NFU + AC is consistent if NFU is consistent, and NF|- not(AC) ???? If it is possible NFU (I don't know it) is obviously not a upperTheory of NF (ok, that the fact because the language is different) and has specific axioms.

Could you explain (in simple english, or in "logic language" :-) ), for your article and the french version, please.

If someone has a response after a long time, may he put it on my french page fr:Utilisateur:Epsilon0, thanks.

Sincerely. --Epsilon0 18:33, 24 May 2007 (UTC)

My interpretation of what is said in the NF page:

Consis(PA) -> Consis(NFU + Infinity + Choice)

(The statement Consis(NFU) -> Consis (NFU + Choice) is not made in that article, so I'm not sure it's correct.)

NF |- not AC

Any "model" of NF also models NFU

— Arthur Rubin | (talk) 20:52, 24 May 2007 (UTC)

Ok, I understand if "Any "model" of NF also models NFU". Thank you --Epsilon0 19:35, 30 May 2007 (UTC) (who has probably an Erdős number of epsilon0 ;) ).

Maybe I'm wrong, but since you can do arithmetic in NFU, doesn't that mean that Consis(NFU)->Consis(PA)? And therefore, by transitivity, Consis(NFU)->Consis(NFU+Infinifty+Choice)? In either case, Holmes does assert this claim. Phill 11:00, 8 July 2007 (UTC)