Definition:Boolean Fiber

Definition

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

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

Then $f$ has two fibers:

$(1): \quad$ The fiber of $\F$ under $f$, defined as $\map {f^{-1} } \F = \set {x \in X: \map f x = \F}$

$(2): \quad$ The fiber of $\T$ under $f$, defined as $\map {f^{-1} } \T = \set {x \in X: \map f x = \T}$.

These fibers are called boolean fibers.

Also see

The fiber of $\T$ is often referred to as the fiber of truth.