Implications

We have the following indirect implication of form equivalence classes:

31 \(\Rightarrow\) 104
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
31 \(\Rightarrow\) 34 clear
34 \(\Rightarrow\) 104 clear

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

Howard-Rubin Number Statement
31:

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

34:

\(\aleph_{1}\) is regular.

104:

There is a regular uncountable aleph. Jech [1966b], p 165 prob 11.26.

Comment:

Back