2
$\begingroup$

I have a question about the following:

enter image description here

I think this should say "... if $I$ finite or if there exists a well-order ..." because if $I$ is a set like this enter image description here

also lets one disjointify $A_i$ with $i \in \{a,b,c,d\}$. Or am I missing something? Thanks!

  • 1
    $I$ is finite or admits a well-order if and only if $I$ admits a well-order. – 2012-10-22

1 Answers 1

1

If $I$ is finite, there is a well-ordering of $I$ in ZF. Thus, the finite case is automatically covered by ‘if there exists a wellorder relation on $I$’.

  • 0
    Oh, right. The order it comes with doesn't matter --$I$can pick an index set of same cardinality to index and pick it so that it has a well-order (if possible). In particular, if it's finite, it's in bijection with a subset of $\omega$ and therefore well-ordered. – 2012-10-22