Cfrgtkky

How does not get the $vDash$ flipped to obtain Enderton's tautologically equivalent symbol?

Here is a picture (courtesy of Google Books)

The code might be

documentclass{article}

usepackage{amsmath,amssymb}

usepackage{graphicx}



newcommand{tautimplies}{vDash}

newcommand{tautimplied}{mathrel{text{reflectbox{$vDash$}}}}

newcommand{tauteq}{%

  tautimplies

  mathrel{mspace{1mu}}%

  tautimplied

}



begin{document}



If (Sigma) is singleton ({sigma}), then we write

``(sigma tautimplies tau)'' in place of 

``({sigma} tautimplies tau).'' If both (sigma tautimplies tau) and

(tau tautimplies sigma), then (sigma)  and (tau) are said to be 

emph{tautologically equivalent} (written (sigma tauteq tau)).

For example, in Section 1.0 we encountered the wffs

( (lnot(mathbf{C} lor mathbf{K})) ) and

( ((lnotmathbf{C}) land (lnotmathbf{K})) )

as alternative translations of an English sentence.  We can now assert that

they are tautologically equivalent.



end{document}

I presume you mean the symbol on page 24 of the second edition of Herbert Enderton’s textbook, A Mathematical Introduction to Logic. Something like this symbol is ⧦ (U+29E6), gleichstark in unicode-math, and the following MWE reproduces the passage that defines it:

documentclass[varwidth=10cm, preview]{standalone}

usepackage{mathtools}

usepackage{unicode-math}

usepackage{microtype}



defaultfontfeatures{ Scale = MatchUppercase }

setmainfont[Scale = 1.0]{STIX Two Text}

setmathfont{STIX Two Math}



begin{document}

If (Sigma) is (operatorname{singleton}{σ}), then we write

“(σ vDash τ)” in place of “({σ} vDash τ).” If both (σ vDash τ) and

(τ vDash σ), then (σ)  and (τ) are said to be emph{tautologically

equivalent} (written (σ gleichstark τ)).

For example, in Section 1.0 we encountered the wffs

( left(¬left(symbfup C ⋁ symbfup Kright)right) ) and

( left(left(¬symbfup Cright) ⋀ left(¬symbfup Kright)right) )

as alternative translations of an English sentence.  We can now assert that

they are tautologically equivalent.

end{document}

This version of it is somewhat narrower than the one in the text, but you can look for a wider version in another font. You might also be able to use this definition:

newcommandtautequiv{mathrel{vDash mkern -2.5mu Dashv}}

Which with STIX Two Math as your math font, gives:

Some math fonts lack a usable Dashv, in which case you can glue a reflectbox{$vDash$} instead:

documentclass[varwidth=10cm, preview]{standalone}

usepackage{mathtools}

usepackage{unicode-math}

usepackage{microtype}

usepackage{graphicx}



defaultfontfeatures{ Scale = MatchUppercase }

setmainfont[Scale = 1.0]{TeX Gyre Pagella}

setmathfont{Asana Math}



newcommandtautimpl{vDash}

newcommandtautequiv{mathrel{vDash mkern -2.25mu

                               mathrel{reflectbox{ensuremathvDash}}}}

%newcommandtautequiv{gleichstark}



begin{document}

If (Sigma) is (operatorname{singleton}{σ}), then we write

“(σ tautimpl τ)” in place of “({σ} tautimpl τ).” If both

(σ tautimpl τ) and (τ tautimpl σ), then (σ)  and (τ) are said to be

emph{tautologically equivalent} (written (σ tautequiv τ)).

For example, in Section 1.0 we encountered the wffs

( left(¬left(symbfup C ⋁ symbfup Kright)right) ) and

( left(left(¬symbfup Cright) ⋀ left(¬symbfup Kright)right) )

as alternative translations of an English sentence.  We can now assert that

they are tautologically equivalent.

end{document}

To the best of my limited German, gleich stark literally means “equally strong” but connotes “very balanced.”

If you need to use PDFTeX rather than LuaLaTeX or XeLaTeX, try loading the stix2 package, replacing symbfup with mathbf, and possibly spelling out the remaining non-ASCII symbols.