The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.research

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 2,637
Registered: 1/8/12
Well Ordering Everything
Posted: May 7, 2014 8:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.