Axiom Of Choice

Statement:

\(C(LO,\infty)\): Every linearly ordered family of non-empty sets has a choice function.

Howard_Rubin_Number: 202

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:
Truss-1978: The axiom of choice for linearly ordered families

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 3, 40, 41, 45-n, 67, 91, 100, 121, 133, 152, 192, 193, 181, 260, 88, 323, 344, 398, 1,

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Complete List of Equivalent Forms

Howard-Rubin Number	Statement	References
202 A	\(H(TR\&C,P)\): If \((X,R)\) is a transitive, connected relation. Then \(X\) has a \(\subseteq\)-maximal partially ordered subset.	Harper-Rubin-1976 Note [39]

Form Classes

Complete List of Equivalent Forms