Axiom Of Choice

We have the following indirect implication of form equivalence classes:

27 \(\Rightarrow\) 27 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
27 \(\Rightarrow\) 27	Zermelo's Axiom of Choice, Moore, 1982, 36

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

Howard-Rubin Number	Statement
27:	\((\forall \alpha)( UT(\aleph_{0},\aleph_{\alpha}, \aleph_{\alpha}))\): The union of denumerably many sets each of power \(\aleph_{\alpha }\) has power \(\aleph_{\alpha}\). Moore, G. [1982], p 36.
27:	\((\forall \alpha)( UT(\aleph_{0},\aleph_{\alpha}, \aleph_{\alpha}))\): The union of denumerably many sets each of power \(\aleph_{\alpha }\) has power \(\aleph_{\alpha}\). Moore, G. [1982], p 36.

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