Axiom Of Choice

We have the following indirect implication of form equivalence classes:

191 \(\Rightarrow\) 189 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
191 \(\Rightarrow\) 189	Injectivity, projectivity and the axiom of choice, Blass, A. 1979, Trans. Amer. Math. Soc.

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

Howard-Rubin Number	Statement
191:	\(SVC\): There is a set \(S\) such that for every set \(a\), there is an ordinal \(\alpha\) and a function from \(S\times\alpha\) onto \(a\).
189:	\(EI\ Ab\): For every Abelian group \(A\) there is an injective Abelian group \(G\) and a one to one homomorphism from \(A\) into \(G\).

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