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Topic: Well Ordering Everything
Replies: 1   Last Post: May 8, 2014 8:24 AM

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William Elliot

Posts: 1,494
Registered: 1/8/12
Well Ordering Everything
Posted: May 7, 2014 8:25 AM
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For all A, (A is well orderable implies P(A) is well orderable). . (P)
Within ZF, does P imple every set is well orderable?

Define by transfinite induction
V_eta = { P(V_xi) | xi < eta }
or equivallently
V_0 = emptyset;  V_(pi+1) = P(V_pi)
V_eta = \/{ V_xi | xi < eta }, eta limit ordinal
Within ZF, does P imply for all eta, V_eta is well orderable?

These two problems are equivalent.



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