Statement:

Partition Principle:  If \(S\) is a partition of \(M\), then \(S \precsim M\).

Howard_Rubin_Number: 101

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-1947: Sur une proposition qui entraine l'existence des ensembles non mesurables

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 30, 7, 14, 43, 40, 93, 100, 205, 347, 101, 1,

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Complete List of Equivalent Forms

Howard-Rubin Number Statement References
101 A

For all sets \(x\) and \(y\), \(x \precsim^* y\) implies \(x\precsim y\).

Lindenbaum-Tarski-1926
Note [69]