Implications

We have the following indirect implication of form equivalence classes:

363 \(\Rightarrow\) 273
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
363 \(\Rightarrow\) 364 Zermelo's Axiom of Choice, Moore, 1982, page 325
364 \(\Rightarrow\) 273 clear

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

Howard-Rubin Number Statement
363:

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

364:

In \(\Bbb R\), there is a measurable set that is not Borel.  G. Moore [1982], p 325.

273:

There is a subset of \({\Bbb R}\) which is not Borel.

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