Axiom Of Choice

Statement:

\(C(\infty,WO)\): Every set of non-empty, well orderable sets has a choice function.
Moore, G. [1982], p 125.

Howard_Rubin_Number: 60

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

This form's transferability is: Transferable

This form's negation transferability is: Negation Transferable

Article Citations:

Book references
The Axiom of Choice, Jech, T., 1973b
Zermelo's Axiom of Choice, Moore, G.H., 1982

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 30, 99, 5, 10, 76, 253, 289, 304, 13, 17, 31, 32, 125, 62, 60, 46-K, 47-n, 45-n, 84, 85, 118, 126, 133, 155, 156, 165, 200, 213, 231, 290, 291, 296, 299, 300, 322, 323, 329, 369, 380, 384, 65, 157, 105, 106, 131, 355, 79, 97, 1, 59-le,

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Complete List of Equivalent Forms

Howard-Rubin Number	Statement	References
60 A	\((\forall\alpha) C(\infty,\aleph_{\alpha})\): For every ordinal \(\alpha\), every family of sets each with power \(\aleph_{\alpha }\) has a choice function.

Form Classes

Complete List of Equivalent Forms