Verum

Definition

Verum

The verum, written $\top$, is the nullary logical constant that is true under every interpretation:

$$v(\top )=\text{true}\text{for every interpretation }v.$$

It is the canonical tautology: a formula that needs no atoms yet is always true. In the entailment definitions the truth value true is written $v(\top )$, as in $v(F)=v(\top )$.

Alternative symbols: $\text{true},\text{T},\text{t},1,\text{w},\dots$