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In type theory judgements are often presented with the following syntax:

enter image description here

My question is what is that symbol in the middle called? All the papers I've found seem to use an image rather than a unicode character so I can't look it up. I've also not found any type-theory reference which says what that symbol is (they explain what it means however).

So what character is that symbol and what is its proper name?

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  • $\begingroup$ Note that $\models$ \models is also often used in logics. $\endgroup$
    – Raphael
    Jun 22, 2012 at 9:37
  • $\begingroup$ @Raphael: $\models$ is used for semantic relationships. $\vdash$ is used for syntactic relationships, such as in proof systems. $\endgroup$ Jun 22, 2012 at 9:43
  • $\begingroup$ @DaveClarke: Of course, I did not want to suggest otherwise. My intention was to leave the trail to $\models$ here, too, as you might also want to type that one if you do logics. (I know we did some weird foo before knowing \models...) $\endgroup$
    – Raphael
    Jun 22, 2012 at 9:49
  • $\begingroup$ It's a good trail to follow. $\endgroup$ Jun 22, 2012 at 9:56
  • $\begingroup$ Yes, that symbol appears often as well. These comments save me another question about it. :) $\endgroup$ Jun 23, 2012 at 3:46

2 Answers 2

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It's called a "turnstile". See the Wikipedia article.

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Detexify

Draw the character on Detexify to see what (La)TeX command generates it.

Oddly, I can't get Detexify to recognize this character. \vdash comes up eventually, but with a very bad score no matter how well I try to draw it.

Shapecatcher

Draw the character on Shapecatcher to see what it is in Unicode. It's U+22A2 RIGHT TACK (⊢).

The usual name in math is turnstile. In this context, it's sometimes called the inference symbol or the deduction symbol. The $\Gamma$ on the left is a context or environment.

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  • $\begingroup$ Shapecatcher is nice. So many symbols. I also trained Detexify until it now comes up near the top. $\endgroup$ Jun 22, 2012 at 3:03
  • $\begingroup$ I couldn't help but try Detexify. I couldn't get it to recognise $\vdash$ either. Grrr. $\endgroup$ Jun 22, 2012 at 9:43
  • $\begingroup$ Too many badly drawn crosses trained. $\endgroup$
    – Raphael
    Jun 22, 2012 at 9:51

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