Implications

We have the following indirect implication of form equivalence classes:

317 \(\Rightarrow\) 153
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
317 \(\Rightarrow\) 14 Limitations on the Fraenkel-Mostowski method of independence proofs, Howard, P. 1973, J. Symbolic Logic
14 \(\Rightarrow\) 153 The Baire category property and some notions of compactness, Fossy, J. 1998, J. London Math. Soc.

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

Howard-Rubin Number Statement
317:

Weak Sikorski Theorem:  If \(B\) is a complete, well orderable Boolean algebra and \(f\) is a homomorphism of the Boolean algebra \(A'\) into \(B\) where \(A'\) is a subalgebra of the Boolean algebra \(A\), then \(f\) can be extended to a homomorphism of \(A\) into \(B\).
14:

BPI: Every Boolean algebra has a prime ideal.

153:

The closed unit ball of a Hilbert space is compact in the weak topology.

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