Description:
Form 385 implies Form 70
Content:
We give a proof that
Form 385 (Every proper
filter with a countable base over a set \(S\) (in \({\cal P}(S)\)) can
be extended to an ultrafilter) implies Form 70 (There is a non-trivial ultrafilter on \(\omega\).)
It is sufficient to show that there is a filter on \(\omega\) with a countable base. For each \(n\in\omega\)
let \(x_{n} = \{m\in\omega: m\geq n\}\). Then, \(X = \{x_n: n\in\omega\}\)
is a countable set which is a base for a filter \(\cal F\) on \(\omega\).
Howard-Rubin number:
150
Type:
Proof
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