I'd like to know ow can i type this symbol like on image in math mode.
Thank you a lot.
You're interested in declaring a new math operator. For this, there exists \DeclareMathOperator (provided by amsmath):
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\VDash}{\vdash}
\begin{document}
See $\VDash_M^*$, or
\[
\VDash_M^* abc.
\]
\end{document}
Also see What is the difference of \mathop, \operatorname and \DeclareMathOperator? for other options if you don't want to declare a new term.
You can do this at TeX level:
\def\Vdash{\mathop{\vdash}}
$\Vdash_M^* abc$ and
$$
\Vdash_M^* abc.
$$
\bye
– Oggy Mar 12 '18 at 19:29$(q_0,\Delta \omega \Delta^\omega, 0) \Vdash_M^* abc (q_f, \gamma, n)$$\displaystyle (q_0,\Delta \omega \Delta^\omega, 0) \Vdash_M^* abc (q_f, \gamma, n)$. Of course, this will affect the line height. – Werner Mar 12 '18 at 19:30