Implications

We have the following indirect implication of form equivalence classes:

97 \(\Rightarrow\) 97
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
97 \(\Rightarrow\) 97 The Axiom of Choice, Jech, 1973b, page 154

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

Howard-Rubin Number Statement
97:

Cardinal Representatives: For every set \(A\) there is a function \(c\) with domain \({\cal P}(A)\) such that for all \(x, y\in {\cal P}(A)\), (i) \(c(x) = c(y) \leftrightarrow x\approx y\) and (ii) \(c(x)\approx x\).  Jech [1973b] p 154.

97:

Cardinal Representatives: For every set \(A\) there is a function \(c\) with domain \({\cal P}(A)\) such that for all \(x, y\in {\cal P}(A)\), (i) \(c(x) = c(y) \leftrightarrow x\approx y\) and (ii) \(c(x)\approx x\).  Jech [1973b] p 154.

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