[FOM] A question on Zorn's lemma

[Rupert McCallum]

It's true that any chain can be well-ordered, but this well-ordering
won't necessarily agree with the ordering induced by that on the
original poset. So it is a priori possible that your amended statement
is false but that Zorn's lemma is still true. 

--- Manuel Ojeda Aciego <aciego at ctima.uma.es> wrote:

> Dear colleagues,
> 
> This is a question about the validity of a version of Zorn's lemma:
> 
> The usual statement of Zorn's lemma says:
> 
> "Every nonempty poset in which every totally ordered subset has an  
> upper bound has at least a maximal element."
> 
> Taking into account that, by the well-ordering principle, any chain  
> can be well-ordered, the alternative statement is the following:
> 
> "Every nonempty poset in which every transfinite sequence has an  
> upper bound has at least a maximal element."
> 
> Perhaps some subscriber has considered this possibility and can  
> provide a (dis)proof of this alternative statement.
> 
> Best regards,
> 
> 
> 
> 
> ---
>   Manuel Ojeda-Aciego          Phone: +34 952 132 871
>   Dept. Applied Mathematics    Fax:   +34 952 132 766 (or 46)
>   Computer Science Faculty    http://sevein.matap.uma.es/~aciego
>   University of Malaga, SPAIN
> 
> 
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