Form equivalence class Howard-Rubin Number: 218
Statement:
Existence of Complementary Subspaces: For every field \(F\), every vector space \(V\) over \(F\) has the property that if \(S\subseteq V\) is a subspace of \(V\), then there is a subspace \(S'\subseteq V\) such that \(S\cap S'= \{0\}\) and \(S\cup S'\) generates \(V\). H. Rubin/J. Rubin [1985], pp 123ff, Theorems 6.36, 6.37, and 6.38.
Howard-Rubin number: 218 A
Citations (articles):
Bleicher [1964]
Some theorems on vector spaces and the axiom of choice
Bleicher [1965]
Multiple choice axioms and the axiom of choice for finite sets
Connections (notes): Note [161]
References (books): Book: Equivalents of the Axiom of Choice II, Rubin-Rubin, [1985]
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