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Give a family of elements $\left(v_{1},\ldots,v_{n}\right)$ (where $v_{1},\ldots,v_{n}$ are just some sets), how many vector spaces are there, such that this family is a basis for that vector space ?

For example, if $n=1$ and $\left(v_{1}\right)=(1)$, there are at least two vector spaces, namely $\mathbb{Q}$ and $\mathbb{R}$ over themselves (as fields), such that this is a basis.

Is there even a reasonable way to answer this ?

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    This is not really a question in set theory.2012-05-17

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