[FOM] Global well ordering versus axiom scheme of collection

Colin McLarty colin.mclarty at case.edu
Tue Aug 14 05:32:22 EDT 2012

Over ZF[0] (which is ZF without the power set axiom), the axiom scheme
of replacement does not imply that of collection.  But ZF[0] with a
well ordering of the universe does, of course, since you can take the
'minimal' exemplar from each class.

In the places where I use a well ordering of the universe, I could as
well use collection.  I wonder if people can suggest reasons to prefer
one approach or the other.

It seems to me that collection is no more constructive or predicative
than a global well ordering.   And since this is all equiconsistent
with Z_2, conceptual concerns seem unpersuasive to me here.  But I
wonder if I am missing important differences.

best, Colin

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