Implications

We have the following indirect implication of form equivalence classes:

147 \(\Rightarrow\) 362
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
147 \(\Rightarrow\) 91 The axiom of choice in topology, Brunner, N. 1983d, Notre Dame J. Formal Logic
note-26
91 \(\Rightarrow\) 361 Equivalents of the Axiom of Choice II, Rubin, 1985, theorem 5.7
361 \(\Rightarrow\) 362 Zermelo's Axiom of Choice, Moore, 1982, page 325

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

Howard-Rubin Number Statement
147:

\(A(D2)\):  Every \(T_2\) topological space \((X,T)\) can be covered by a well ordered family of discrete sets.

91:

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

361:

In \(\Bbb R\), the union of a denumerable number of analytic sets is analytic. G. Moore [1982], pp 181 and 325.

362:

In \(\Bbb R\), every Borel set is analytic. G. Moore [1982], pp 181 and 325.

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