Definition:Boolean Fiber

Definition

Let $\Bbb B = \left\{{T, F}\right\}$ be a boolean domain.

Let $f : X \to \Bbb B$ be a boolean-valued function.

Then $f$ has two fibers:

• The fiber of $F$ under $f$, defined as $f^{-1} \left({F}\right) = \left\{{x \in X: f \left({x}\right) = F}\right\}$
• The fiber of $T$ under $f$, defined as $f^{-1} \left({T}\right) = \left\{{x \in X: f \left({x}\right) = T}\right\}$.

These fibers are called boolean fibers.

The fiber of $T$ is known as the fiber of truth.