Axiom Of Choice

We have the following indirect implication of form equivalence classes:

126 \(\Rightarrow\) 126 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
126 \(\Rightarrow\) 126

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

Howard-Rubin Number	Statement
126:	\(MC(\aleph_0,\infty)\), Countable axiom of multiple choice: For every denumerable set \(X\) of non-empty sets there is a function \(f\) such that for all \(y\in X\), \(f(y)\) is a non-empty finite subset of \(y\).
126:	\(MC(\aleph_0,\infty)\), Countable axiom of multiple choice: For every denumerable set \(X\) of non-empty sets there is a function \(f\) such that for all \(y\in X\), \(f(y)\) is a non-empty finite subset of \(y\).

Comment:

Back