Almost free non-Archimedean Banach k-vector spaces are free when their cardinality satisfies ℵ₁-strong compactness or weak compactness.
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Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals
Almost free non-Archimedean Banach k-vector spaces are free when their cardinality satisfies ℵ₁-strong compactness or weak compactness.