Implications

We have the following indirect implication of form equivalence classes:

133 \(\Rightarrow\) 363
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
133 \(\Rightarrow\) 90 Dedekind-Endlichkeit und Wohlordenbarkeit, Brunner, N. 1982a, Monatsh. Math.
90 \(\Rightarrow\) 91 The Axiom of Choice, Jech, 1973b, page 133
91 \(\Rightarrow\) 363 Equivalents of the Axiom of Choice II, Rubin, 1985, theorem 5.7

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

Howard-Rubin Number Statement
133:  

Every set is either well orderable or has an infinite amorphous subset.

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.

363:

There are exactly \(2^{\aleph_0}\) Borel sets in \(\Bbb R\). G. Moore [1982], p 325.

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