Turnstile

A rotating mechanical device that controls and counts passage between public areas, especially one that only allows passage after a charge has been paid.

A similar device in a footpath to allow people through one at a time while preventing the passage of cattle.

The \vdash symbol used to represent logical entailment (deducibility relation), especially of the syntactic type; i.e., syntactic consequence. (Such symbol can be read as "prove(s)" or "give(s)". )