a structure of four horizontally revolving arms pivoted atop a post and set in a gateway or opening in a fence to allow the controlled passage of people.
a similar device set up in an entrance to bar passage until a charge is paid, to record the number of persons passing through, etc.

1635–45; turn + stile1

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World English Dictionary
turnstile (ˈtɜːnˌstaɪl)
1.  a mechanical gate or barrier with metal arms that are turned to admit one person at a time, usually in one direction only
2.  any similar device that admits foot passengers but no large animals or vehicles
3.  logic Also called: gatepost a symbol of the form ̃⊢, ⊨, or ⊩, used to represent logical consequence when inserted between expressions to form a sequent, or when prefixed to a single expression to indicate its status as a theorem

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1643, from turn + stile.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
From there to the subway, where a wave of another smart card over a turnstile
  pays the fare.
Buzz for entry and place your order at the elaborate turnstile designed to let
  the nuns maintain their privacy.
Many of the houses in the area even had a turnstile as an entry to keep the
  curious horses from sneaking in for a snack.
In the camp store the first section you come to through the turnstile is the
  liquor department.
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