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According to Wikipedia, A powerful and nontrivial metatheorem states that any theorem of 𝟐 holds for all Boolean algebras. Conversely, an identity that holds for an arbitrary nontrivial Boolean algebra also holds in 𝟐. Hence all the mathematical content of Boolean algebra is captured by 𝟐. What this means is that if $\phi = \psi$ is an equation in ...


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I am not used to this definition. Instead, the definition I am used to states that a system of boolean equations has the form $$\begin{align*} f_1(x_1,\dots,x_n)&=0\\ \vdots\\ f_m(x_1,\dots,x_n)&=0. \end{align*}$$ where $x_1,\dots,x_n$ are boolean variables and $f_1,\dots,f_m$ are boolean functions. The values $v_1,\dots,v_n$ are a solution to the ...


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