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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: Parents and Children''
by marijke on 2006-02-16 12:31:20 |
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| > You can omit premise 1) - the 0 element has no ancestors,
> so premise 2) applies.
Yes :)
> I have the strong suspicion that the following is also true..
> maybe you find a proof? Guess it's easy, but I'm tired of proving.
> __________________
>
> Thm. Let (L, <) be a poset. The following two are equivalent.
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> (i) (L, <) is a tree in the set-theoretic sense.
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> (ii) (L, <) is a trans-inductive evolution poset.
Thought i had a proof, but it's a bit more tricky. I'll think about it.
--regards, marijke
http://web.mat.bham.ac.uk/marijke/ |
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