Implications

We have the following indirect implication of form equivalence classes:

245 \(\Rightarrow\) 19
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
245 \(\Rightarrow\) 34 The monadic theory of \(\omega_1\), Litman, A. 1976, Israel J. Math.
34 \(\Rightarrow\) 19 Sur les fonctions representables analytiquement, Lebesgue, H. 1905, J. Math. Pures Appl.

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

Howard-Rubin Number Statement
245:

There is a function \(f :\omega_1\rightarrow \omega^{\omega}_1\) such that for every \(\alpha\), \(0 < \alpha < \omega_1\), \(f(\alpha )\) is a function from \(\omega\) onto \(\alpha\).

34:

\(\aleph_{1}\) is regular.

19:

A real function is analytically representable if and only if it is in Baire's classification. G.Moore [1982], equation (2.3.1).

Comment:

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