What is the LaTeX symbol for “forking independent” (model theory)?

Question

I am looking for a way to set the symbol for "forking independent" (for example, see "Essential Stability Theory", Steven Buechler, p.217). It looks a bit like an anchor or an upside-down 'T' with a curved bar.

Answer 1

I don't think this symbol exists in any of the typical packages, so it looks like you'll have to roll your own. You can combine the \smile symbol from the amssymb package with a \vert line for this. Here's one way to do it, based on Overlay symbol with another and \subseteq + \circ as a single symbol ("open subset").

\documentclass{article}
\usepackage{amsmath,amssymb}
\def\forkindep{\mathrel{\raise0.2ex\hbox{\ooalign{\hidewidth$\vert$\hidewidth\cr\raise-0.9ex\hbox{$\smile$}}}}}

\begin{document}
The symbol by itself: $\forkindep$

The symbol used with \verb|\underset|: $A \underset{C}{\forkindep} B$
\end{document}

Answer 2

A variation, using \oalign instead of \ooalign; the spacing will be right only if the symbol is treated as a binary relation

\documentclass[a4paper]{article}
\newcommand{\forkindep}[1][]{%
  \mathrel{
    \mathop{
      \vcenter{
        \hbox{\oalign{\noalign{\kern-.3ex}\hfil$\vert$\hfil\cr
              \noalign{\kern-.7ex}
              $\smile$\cr\noalign{\kern-.3ex}}}
      }
    }\displaylimits_{#1}
  }
}

\begin{document}
$A\forkindep[C]B$
\[
A\forkindep[C]B
\]
\end{document}

This will typeset the (optional) argument as a subscript in text style and below the symbol in display style.

Answer 3

Unicode has that symbol at 0x2ADD, so you could do with XeTeX something like:

\XeTeXmathchardef\nonforking"3"2"2ADD
% ^take from symbol family ("2), and define as relation ("3)
$ A \nonforking_C B $
$\displaystyle A \mathop{\nonforking}_C B $ % note: changed from rel to op

This would of course need the appropriate fonts and such loaded (with unicode-math for example, it is already defined as \forksnot)

Answer 4

Thanks to the arXiv, one can find out what Buechler himself has used (and other model theorists in the area). Downloading the source of this paper and looking in its preamble, one finds:

\def\dnfo{\;\raise.2em\hbox{$\mathrel|\kern-.9em\lower.4em\hbox{$\smile$}$}}

\def\dnf#1{\lower.9em\hbox{$\buildrel\dnfo\over{ \scriptstyle  #1}$}}

\def\indep#1#2#3{\hbox{\mathsurround=0pt$#1 \  \dnf{#2} \ #3$}}

(among several related definitions). Then \indep{A}{C}{B} produces your example.

Answer 5

Including the package \usepackage{MnSymbol} you can also use \downfree (or \ndownfree respectively if you want to talk about dependent sets) for the desired symbol.