Statement:

(For \(n\in\omega-\{0,1\}\)) If all \(\varSigma^{1}_{n}\), Dedekind finite subsets of \({}^{\omega }\omega\) are finite, then all \(\varPi^1_n\) Dedekind finite subsets of \({}^{\omega} \omega\) are finite.

Howard_Rubin_Number: 199(\(n\))

Parameter(s): This form depends on the following parameter(s): \(k\), \(k\): integer \( > 1 \)

This form's transferability is: Transferable

This form's negation transferability is: Negation Transferable

Article Citations:
Kanovei-1978: The non-emptyness of classes in axiomatic set theory

Book references

Note connections:
Note 57 Truss [1995] studies the various structures an amorphous set can carry.
Note 61 Kanovei [1979] studies the relationships between \(AC(K)\)  and \(DC(K)\)

The following forms are listed as conclusions of this form class in rfb1:

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