Statement:
Every field \(F\) and every vector space \(V\) over \(F\) has the property that each linearly independent set \(A\subseteq V\) can be extended to a basis. H.Rubin/J.~Rubin [1985], pp 119ff.
Howard_Rubin_Number: 109
Parameter(s): This form does not depend on parameters
This form's transferability is: Not Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
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
Blass-1984a: Existence of a basis implies the axiom of choice
Book references
Equivalents of the Axiom of Choice II, Rubin, J., 1985
Note connections: