Axiom Of Choice

Statement:

\(PW\): The power set of a well ordered set can be well ordered.

Howard_Rubin_Number: 91

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:

Book references
The Axiom of Choice, Jech, T., 1973b
Equivalents of the Axiom of Choice II, Rubin, J., 1985

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 99, 76, 210, 37, 125, 47-n, 90, 91, 96, 103, 118, 130, 145, 147, 152, 155, 156, 163, 243, 190, 173, 236, 200, 217, 235, 273, 237, 240, 241, 249, 285, 293, 290, 291, 305, 313, 322, 330, 349, 350, 356, 357, 361, 363, 382, 244, 119, 151, 157, 106, 355, 238, 294, 309, 337, 79, 97, 1, 183-alpha, 59-le, 136-k, 220-p, 288-n,

Howard-Rubin Number	Statement	References
91 A	\(A(S,W1)\): For every \(T_2\) topological space \((X,T)\) if \(X\) has a dense well ordered subset, then \(T\) is well ordered. (Clear)	Brunner [1983d] Note [26]
91 B	The Axiom of Choice for Pure Sets. If \(X\) is a set of non-empty sets and there are no atoms in the transitive closure of \(X\), then \(X\) has a choice function.	Note [75]