Implications

We have the following indirect implication of form equivalence classes:

296 \(\Rightarrow\) 127
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
296 \(\Rightarrow\) 64 clear
64 \(\Rightarrow\) 127 Amorphe Potenzen kompakter Raume, Brunner, N. 1984b, Arch. Math. Logik Grundlagenforschung

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
296:

Part-\(\infty\): Every infinite set is the disjoint union of infinitely many infinite sets.

64:

\(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.)

127:

An amorphous power of a compact \(T_2\) space, which as a set is well orderable, is well orderable.

Comment:

Back