# Enderton's tautologically equivalent symbol

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

• Do you mean the one on page 24 of his A Mathematical Introduction to Logic? Jan 22 '19 at 4:51
• In the future, a good resource to check out is detexify. If you don't find it there, it’d usually be helpful to draw it as best you can, to give us the best chance of knowing what you mean. Jan 22 '19 at 4:52
• Are you interested in something like this?
– Werner
Jan 22 '19 at 4:59
• Here’s the free preview, but I found it. Jan 22 '19 at 4:59

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
$$((\lnot\mathbf{C}) \land (\lnot\mathbf{K}))$$
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
$$\left(¬\left(\symbfup C ⋁ \symbfup K\right)\right)$$ and
$$\left(\left(¬\symbfup C\right) ⋀ \left(¬\symbfup K\right)\right)$$
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:

\newcommand\tautequiv{\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}

\newcommand\tautimpl{\vDash}
\newcommand\tautequiv{\mathrel{\vDash \mkern -2.25mu
\mathrel{\reflectbox{\ensuremath\vDash}}}}
%\newcommand\tautequiv{\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
$$\left(¬\left(\symbfup C ⋁ \symbfup K\right)\right)$$ and
$$\left(\left(¬\symbfup C\right) ⋀ \left(¬\symbfup K\right)\right)$$
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.

• +1, but Germans would not agree on "strongly equal". It is more "equally strong"… Jan 22 '19 at 6:11

Here's my solution:

\sigma |\!\!\!=\!\!\!|\, \tau


gives It's not perfect, but only when zoomed in; in a smaller size it looks fine. Benefits include literally not needing any packages and the code looking really cool (or disgusting, depending on how you look at it).

Here's an alternative one that looks better when zoomed in:

\models\!\mid

• In the book, the symbol is distinctly in two separate parts, not joined. However, it is very likely the same as \gleichstark, defined in unicode-math, which has a longer joining component. Oct 5 at 0:26