Re: A simple question?


Jules wrote:
MoeBlee wrote:
zuhair wrote:
Hi,

For w={ 0,1,2,3,....} , is P(w) a well ordered set?

You mean the power set of omega?

Your question is not complete.

Under what axioms?

A set is well ordered if there is a well ordering of the set.

I do not think this is correct. Well-ordered can only apply to a
totally ordered set. For example, the real numbers are not well
ordered, but there is a well-ordering of the real numbers which is not
the standard ordering.

Well, the standard ordering clearly isn't a well-ordering.

What is this well-ordering of the reals, then?

--- Christopher Heckman

I think the real question here is: what ordering are you assigning to
P(w)?

With the axiom of choice added to the ZF axioms, every set has a well
ordering.

As I understand, ZF without the axiom of choice cannot prove that the
power set of omega has a well ordering.

MoeBlee

.

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