Implications

We have the following indirect implication of form equivalence classes:

90 \(\Rightarrow\) 371
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
90 \(\Rightarrow\) 91 The Axiom of Choice, Jech, 1973b, page 133
91 \(\Rightarrow\) 79 clear
79 \(\Rightarrow\) 371 S´eminaire d’Analyse 1994, Morillon, 1993,

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
90:

\(LW\):  Every linearly ordered set can be well ordered. Jech [1973b], p 133.

91:

\(PW\):  The power set of a well ordered set can be well ordered.

79:

\({\Bbb R}\) can be well ordered.  Hilbert [1900], p 263.

371:

There is an infinite, compact, Hausdorff, extremally disconnected topological space.  Morillon [1993].

Comment:

Back