Axiom Of Choice

Statement:

$C(\aleph_{0},\le 2^{\aleph_{0}})$ : Every denumerable collection of non-empty sets each with power $\le 2^{\aleph_{0}}$ has a choice function.

Howard_Rubin_Number: 16

Parameter(s): This form does not depend on parameters

This form's transferability is: Unknown

This form's negation transferability is: Negation Transferable

Article Citations:
Sierpi'nski-1918: L’axiome de M. Zermelo et son rˆole dans la th´eorie des ensembles et l’analyse

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 29, 94, 304, 6, 13, 16, 125, 53, 69, 64, 84, 124, 127, 128, 146, 155, 156, 177, 194, 200, 267, 290, 291, 352, 390, 157, 278, 131, 355, 97, 59-le,

Back

Complete List of Equivalent Forms

Howard-Rubin Number	Statement	References
16 A	$C(\aleph_0,2^{\aleph_0})$ : Every denumerable collection of non-empty sets each with power $2^{\aleph_{0}}$ has a choice function. \ac{Sierpi\'nski} \cite{1918} and note 160.

Form Classes

Complete List of Equivalent Forms