Implications

We have the following indirect implication of form equivalence classes:

50 \(\Rightarrow\) 298
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
50 \(\Rightarrow\) 14 A survey of recent results in set theory, Mathias, A.R.D. 1979, Period. Math. Hungar.
14 \(\Rightarrow\) 298 Some propositions equivalent to the Sikorski extension theorem for Boolean algebras, Bell, J.L. 1988, Fund. Math.
Projective topological spaces, Gleason, A.M. 1958, Illinois J. Math.

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

Howard-Rubin Number Statement
50:

Sikorski's  Extension Theorem: Every homomorphism of a subalgebra \(B\) of a Boolean algebra \(A\) into a complete Boolean algebra \(B'\) can be extended to a homomorphism of \(A\) into \(B'\). Sikorski [1964], p. 141.

14:

BPI: Every Boolean algebra has a prime ideal.

298:

Every compact Hausdorff space has a Gleason cover.

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