4

I'm working on this short paper about cardinal invariants in Cichoń's diagram. I wanted to somehow draw in tex. I have no previous experience in drawing any kind of diagrams in tex. Usinge package amscd and this code:

\begin{equation}\begin{CD}
@. cov(\mathcal{N}) @>>> non(\mathcal{M}) @>>> cof(\mathcal{M}) @>>>
cof(\mathcal{N}) @>>> 2^{\aleph_0}\\
@. @AAA @AAA @AAA @AAA\\
@. @AAA \mathfrak{b} @>>> \mathfrak{d} @. @AAA\\
@. @AAA @AAA @AAA @AAA\\
\aleph_1 @>>> add(\mathcal{N}) @>>> add(\mathcal{M}) @>>> cov(\mathcal{M}) @>>>
non(\mathcal{N})
\end{CD}\end{equation}

I end up with the following result:

enter image description here

Is there any way I can make these sequences of arrows on left and right just 1 long one? Or maybe there's a simpler way to do this?

2
  • I would suggest the tikz-cd package instead. The amscd package is to say the least, minimally documented.
    – Alan Munn
    Dec 13 '20 at 0:33
  • 1
    In the future, when you post a question, please provide a "Minimal Working Example" (MWE) that starts with \documentclass, includes all relevant \usepackage commands, ends with \end{document} and compiles without errors, even if it does not produce your desired output. Welcome to TeX.SX!
    – Sandy G
    Dec 13 '20 at 1:17
7

Here is a solution with tikz-cd.

enter image description here

I used the upright shape for the cardinal characteristics, which is how I've seen them. If you prefer the slanted shape, I recommend you use \mathit{...}. Otherwise the spacing is off. I declared them as math operators for convenience.

\documentclass{article}

\usepackage{mathtools,amsfonts} % mathtools to use \DeclareMathOperator command
\usepackage{tikz-cd}

\DeclareMathOperator{\cov}{cov}
\DeclareMathOperator{\non}{non}
\DeclareMathOperator{\cof}{cof}
\DeclareMathOperator{\add}{add}

\begin{document}

\[
\begin{tikzcd}
    & \cov(\mathcal{N})\arrow[r] & \non(\mathcal{M})\arrow[r] & \cof(\mathcal{M})\arrow[r] & \cof(\mathcal{N})\arrow[r] & 2^{\aleph_0}\\
    & & \mathfrak{b}\arrow[u]\arrow[r] & \mathfrak{d}\arrow[u]\\
\aleph_1\arrow[r] & \add(\mathcal{N})\arrow[uu]\arrow[r] & \add(\mathcal{M})\arrow[r]\arrow[u] & \cov(\mathcal{M})\arrow[r]\arrow[u] & \non(\mathcal{N})\arrow[uu]
\end{tikzcd}
\]

\end{document}
0
6

Just for fun, two alternatives, although I recommend tikz-cd.

Hand made diagram

enter image description here

\documentclass{article}
\usepackage{amsmath,amsfonts}

\begin{document}

\[
\newcommand{\middlecolumn}[1]{%
  \begin{array}{@{}c@{}}
  \big\uparrow \\
  \noalign{\vspace{0.5ex}}
  #1 \\
  \noalign{\vspace{0.5ex}}
  \big\uparrow
  \end{array}%
}
\newcommand{\lto}{{}\longrightarrow{}}
\setlength{\nulldelimiterspace}{0pt}
\begin{array}{@{}*{11}{c@{}}}
&&
\operatorname{cov}(\mathcal{N}) & \lto &
\operatorname{non}(\mathcal{M}) & \lto &
\operatorname{cof}(\mathcal{M}) & \lto &
\operatorname{cof}(\mathcal{N}) & \lto &
2^{\aleph_0} \\
\noalign{\vspace{0.5ex}}
&& \left\uparrow\vphantom{\middlecolumn{\mathfrak{b}}}\right.
&& \middlecolumn{\mathfrak{b}} &
\makebox[0pt]{$\xrightarrow{\hspace{3.5em}}$}
 & \middlecolumn{\mathfrak{d}}
&& \left\uparrow\vphantom{\middlecolumn{\mathfrak{b}}}\right. \\
\noalign{\vspace{0.5ex}}
\aleph_1 & \lto &
\operatorname{add}(\mathcal{N}) & \lto &
\operatorname{add}(\mathcal{M}) & \lto &
\operatorname{cov}(\mathcal{M}) & \lto &
\operatorname{non}(\mathcal{N}) &
\end{array}
\]

\end{document}

Xy-pic

enter image description here

\documentclass{article}
\usepackage{amsmath,amsfonts}
\usepackage[all,cmtip]{xy}

\begin{document}

\[
\xymatrix@R-0.5pc@C-0.8pc{
&
\operatorname{cov}(\mathcal{N}) \ar[r] &
\operatorname{non}(\mathcal{M}) \ar[r] &
\operatorname{cof}(\mathcal{M}) \ar[r] &
\operatorname{cof}(\mathcal{N}) \ar[r] &
2^{\aleph_0} \\
&& \mathfrak{b} \ar[r] \ar[u] & \mathfrak{d} \ar[u] \\
\aleph_1 \ar[r] &
\operatorname{add}(\mathcal{N}) \ar[r] \ar[uu] &
\operatorname{add}(\mathcal{M}) \ar[r] \ar[u] &
\operatorname{cov}(\mathcal{M}) \ar[r] \ar[u] &
\operatorname{non}(\mathcal{N}) \ar[uu]
}
\]

\end{document}

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