amscd and Cichoń's Diagram

Here is a solution with tikz-cd.

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}

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

Hand made diagram

\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

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

\begin{document}

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

\end{document}