A relation symbol representing semantic entailment or model-theoretic forcing in mathematical logic and set theory.
Examples
Logical forcing relation
P \Vdash \varphi \text{ means 'P forces } \varphi\text{'}
Model theory satisfaction
\mathcal{M} \Vdash \forall x(P(x) \rightarrow Q(x))
Forcing in set theory
p \Vdash \text{``}\dot{G} \text{ is a generic filter''}