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We have the following indirect implication of form equivalence classes:

222 \(\Rightarrow\) 223 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
222 \(\Rightarrow\) 223	clear

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

Howard-Rubin Number	Statement
222:	There is a non-principal measure on \(\cal P(\omega)\).
223:	There is an infinite set \(X\) and a non-principal measure on \(\cal P(X)\).

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