Re: Cofinality
- From: Ross <rmillika@xxxxxxxxxxx>
- Date: Wed, 9 Apr 2008 08:11:35 -0700 (PDT)
On Apr 8, 10:30 am, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:
Let S be a linear order.
Let A be a cofinal subset of S. By theorem, we
may assume A is a well ordered cofinal subset.
Is there a C subset A such that C is cofinal
to S and |C| = cof S, the cofinality of S?
As this seems most likely, how would one construct C?
This seems of interest only if S is infinite and singular. How about
find B which witnesses the cofinality of S. Then construct C by
replacing each element of B with the first element of A greater than
that element?
.
- References:
- Cofinality
- From: William Elliot
- Cofinality
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