Definition:Two (Boolean Lattice)

This page is about Two in the context of Boolean Lattice. For other uses, see Two.

Definition

Let $\struct{\mathbf 2, \lor, \land, \neg}$ denote the (Boolean algebra) two where:

$\mathbf 2 := \set {\bot, \top}$

$\top$ denotes the canonical tautology

$\bot$ denotes the canonical contradiction

Define $\preceq$ to be the ordering determined by putting $\bot \preceq \top$.

When endowed with the ordering $\preceq$, $\mathbf 2$ becomes a Boolean lattice, as shown on Two is Boolean Lattice.

The (Boolean lattice) two, is defined as $\struct{\mathbf 2, \lor, \land, \neg, \preceq}$.

Also see

• Two is Boolean Lattice

• Definition:Two (Boolean Algebra), where $\mathbf 2$ is viewed as a Boolean algebra.

• Definition:Two (Category), the category $\mathbf 2$ becomes when viewed as an order category.

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