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Let $G$ be the set of all formulas $\phi(x)$ in the language of such that $ZFC\vdash\exists x\phi(x)$ exists, $ZFC\vdash\phi(x)\rightarrow``x\,\textrm{is a complete Boolean algebra}"$, $ZFC\vdash``\...

There are many equivalent ways to describe Boolean algebras. There are a number of different ways to "minimize" the description. We can: Minimize the number of function symbols. Minimize ...