Form Classes

Statement:

Every linearly ordered Dedekind finite set is finite.

Howard_Rubin_Number: 185

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:
Hickman-1979a: A class of near-finite order types

Book references

Note connections:
Note 94 Relationships between the different definitions of finite

The following forms are listed as conclusions of this form class in rfb1: 171, 10, 76, 324, 7, 9, 13, 18, 53, 57, 64, 84, 98, 124, 126, 127, 128, 146, 154, 177, 185, 198, 200, 216, 293, 328, 358, 390, 278, 131, 314, 288-n, 342-n, 308-p, 373-n,

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Complete List of Equivalent Forms

Howard-Rubin Number Statement References
185 A

If \(X\) is a linearly ordered set and there is neither an increasing nor a decreasing injection \(f:\omega\rightarrow X\), then \(X\) is finite.

Hickman [1979a]