Implications

We have the following indirect implication of form equivalence classes:

27 \(\Rightarrow\) 31
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
27 \(\Rightarrow\) 31 clear

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.

31:

\(UT(\aleph_{0},\aleph_{0},\aleph_{0})\): The countable union theorem:  The union of a denumerable set of denumerable sets is denumerable.

Comment:

Back