[FOM] A question on Zorn's lemma

[Manuel Ojeda Aciego]

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,




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  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