Implications

We have the following indirect implication of form equivalence classes:

101 \(\Rightarrow\) 205
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
101 \(\Rightarrow\) 205 On some weak forms of the axiom of choice in set theory, Pelc, A. 1978, Bull. Acad. Polon. Sci. S'er. Sci. Math. Astronom. Phys.

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

Howard-Rubin Number Statement
101:

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

205:

For all cardinals \(m\) and \(n\), if \(m\le^* n\) and \(\neg (n\le^* m)\) then there is a cardinal \(k \le n\) such that \(m\le^* k\).

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