Implications

We have the following indirect implication of form equivalence classes:

120-K \(\Rightarrow\) 48-K
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
120-K \(\Rightarrow\) 48-K clear

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

Howard-Rubin Number Statement
120-K:

If \(K\subseteq\omega-\{0,1\}\), \(C(LO,K)\): Every linearly ordered set of non-empty sets each of whose cardinality is in \(K\) has a choice function.

48-K:

If \(K\) is a finite subset of \(\omega-\{0,1\}\), \(C(WO,K)\): For every \(n\in K,\) \(C(WO,n)\).

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