Implications

We have the following indirect implication of form equivalence classes:

105 \(\Rightarrow\) 105
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
105 \(\Rightarrow\) 105 The consistency of the axiom of universality for the ordering of cardinals, Forti, M. 1985, J. Symbolic Logic
On the ordering of cardinalities, Jech, T. 1966c, 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
105:

There is a  partially ordered set \((A,\le)\) such that for no set \(B\) is \((B,\le)\) (the ordering  on \(B\) is the usual injective cardinal ordering) isomorphic to \((A,\le)\).

105:

There is a  partially ordered set \((A,\le)\) such that for no set \(B\) is \((B,\le)\) (the ordering  on \(B\) is the usual injective cardinal ordering) isomorphic to \((A,\le)\).

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