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A Boolean algebra is a commutative ring satisfying x²=x for every x, and sometimes required to have a unit; they have characteristic 2. For coding theory (notably dealing with subsets linear subspaces of spaces of Boolean functions), rather use the [coding-theory] or [linear-algebra] tag.
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Proving results about complete Boolean algebras in ZFC using Boolean valued models
You can, for example, show that many standard complete boolean algebras like Cohen algebra cannot be isomorphic to a quotient $\mathcal{P}(X) / I$ for any sigma ideal $I$ over $X$. These results are d …