Implications

• Implications Home
• Code 1 Implications
• Code 2 Implications
• Code 3 Implications
• Code 4 Implications
• Code 5 Implications
• Code 6 Implications
• Complete List
• Search

We have the following indirect implication of form equivalence classes:

110 \(\Rightarrow\) 18 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
110 \(\Rightarrow\) 18	The vector space Kinna-Wagner Principle is equivalent to the axiom of choice, Keremedis, K. 2001a, Math. Logic Quart.

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

Howard-Rubin Number	Statement
110:	Every vector space over \(\Bbb Q\) has a basis.
18:	\(PUT(\aleph_{0},2,\aleph_{0})\):  The union of a denumerable family of pairwise disjoint pairs has a denumerable subset.

Comment: