Statement:
\(MC(\infty,\infty,\mathrm{odd})\): For every set \(X\) of sets such that for all \(x\in X\), \(|x|\ge 1\), there is a function \(f\) such that for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\) and \(|f(x)|\) is odd.
Howard_Rubin_Number: 333
Parameter(s): This form does not depend on parameters
This form's transferability is: Not Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Keremedis-1996a: Bases for vector spaces over the two element field and the axiom of choice
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 333 A | In every vector space \(B\) over the two element field, every subspace of \(B\) has a complementary subspace. |
Keremedis [1996a]
|
| 333 B | Every quotient group of an Abelian group each of whose non-unit elements has order 2 has a set of representatives. |
Keremedis [1996b]
|