Implications

We have the following indirect implication of form equivalence classes:

239 \(\Rightarrow\) 428
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
239 \(\Rightarrow\) 110 clear
110 \(\Rightarrow\) 428 clear

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

Howard-Rubin Number Statement
239:

AL20(\(\mathbb Q\)):  Every vector \(V\) space over \(\mathbb Q\) has the property that every linearly independent subset of \(V\) can be extended to a basis. Rubin, H./Rubin, J. [1985], p.119, AL20.

110:

Every vector space over \(\Bbb Q\) has a basis.

428: \(\exists F\) B\((F)\):  There is a field \(F\) such that every vector space over \(F\) has a basis. \ac{Bleicher} \cite{1964}, \ac{Rubin, H.\/Rubin, J \cite{1985, p.119, B}.

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