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We have the following indirect implication of form equivalence classes:

35 \(\Rightarrow\) 38 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
35 \(\Rightarrow\) 38	Non-constructive properties of the real numbers, Howard, P. 2001, Math. Logic Quart.

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

Howard-Rubin Number	Statement
35:	The union of countably many meager subsets of \({\Bbb R}\) is meager. (Meager sets are the same as sets of the first category.) Jech [1973b] p 7 prob 1.7.
38:	\({\Bbb R}\) is not the union of a countable family of countable sets.

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