Axiom Of Choice

We have the following indirect implication of form equivalence classes:

59-le \(\Rightarrow\) 59-le given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
59-le \(\Rightarrow\) 59-le	A survey of recent results in set theory, Mathias, A.R.D. 1979, Period. Math. Hungar.

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

Howard-Rubin Number	Statement
59-le:	If \((A,\le)\) is a partial ordering that is not a well ordering, then there is no set \(B\) such that \((B,\le)\) (the usual injective cardinal ordering on \(B\)) is isomorphic to \((A,\le)\). Mathias [1979], p 120.
59-le:	If \((A,\le)\) is a partial ordering that is not a well ordering, then there is no set \(B\) such that \((B,\le)\) (the usual injective cardinal ordering on \(B\)) is isomorphic to \((A,\le)\). Mathias [1979], p 120.

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