Reduce/tighter vertical spacing in \underbrace

Question

Lots of questions here about increasing the vertical spacing in underbrace (e.g. Increase vertical space beetwen underbrace bracket and content and Vertical Space between formula and brackets), but none I could find about decreasing it. The following code

% minimal working example (MWE)
\documentclass{article}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{mathtools}
\newcommand{\ring}{\text{ring}}
\newcommand{\alg}{\text{alg}}
\newcommand{\ACF}{\text{ACF}}
\begin{document} 
This also helps determine completions of ACF (ACF not complete theory, because $\mathbb C \models \ACF$ and $\mathbb F_p^\alg \models \ACF$, but the $\mathscr L_\ring$-sentence $\smash{\underbracket[0.2pt]{1+\ldots + 1}_{\scriptscriptstyle p\text{ times}}=0}$ is not satisfied by $\mathbb C$ but satisfied by $\mathbb F_p^\alg$). More explicitly: adding the characteristic $p$ sentence produces a complete theory. 
\end{document}

I think if we can move up the underbracket, and move up the text underneath the underbracket it can all fit in the space between the lines (and definitely so if we say increase line spacing to 1.5 or something).

Answer 1

I copied the \underbracket definition from mathtools.sty and did modifications at two places:

\bgroup \catcode`_=11 \catcode`:=11 \catcode`\@=11
\gdef\MT_underbracket_II:w[#1][#2]#3{%
  \mathop{\vtop{\m@th\ialign{##
    \crcr
      $\hfil\displaystyle{#3}\hfil$%
    \crcr
      \noalign{\kern -.5ex \nointerlineskip}% <<< negative kern here
      \upbracketfill {#1}{#2}%
    \crcr}\kern-.2ex}} % <<< added negative kern here
  \limits}
\egroup

If you want to have equidistant baselineskip in the whole paragraph with underbracket in it, I suggest to set \baselineskip=1.6em.

Edit: If you plan to use your \myunderbracket in the format

\myunderbracket[thickness]{formula}

(like in your example), then you can define:

\def\myunderbracket[#1]#2{%
  \mathop{\vtop{\ialign{##\crcr
      $\hfil\displaystyle{#2}\hfil$%
    \crcr
      \noalign{\kern -.5ex \nointerlineskip}% <<< negative kern here
      \upbracketfill {#1}{.7\fontdimen5\textfont2}%
    \crcr}\kern-.2ex}} % <<< added negative kern here
  \limits}

Answer 2

With TikZ:

\documentclass{article}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{mathtools}
\newcommand{\ring}{\text{ring}}
\newcommand{\alg}{\text{alg}}
\newcommand{\ACF}{\text{ACF}}
\usepackage{tikz}
\usetikzlibrary{positioning}
\newcommand{\myunder}[2]{\tikz[baseline]{\node[inner sep=0pt, anchor=base, baseline](A){$#1$};
  \coordinate (startpoint) at ([xshift=-.05em,yshift=-.3ex]A.south west);
  \coordinate (endpoint) at ([xshift=.05em,yshift=-.3ex]A.south east);
  \draw[line width=0.2pt] ([yshift=3pt]startpoint) -- (startpoint) -- (endpoint) -- ++(0,3pt);
  \node[inner sep=0pt, below=3pt of A.south]{$\scriptscriptstyle #2$};}}
\begin{document} 
With Ti\emph{k}Z:
This also helps determine completions of ACF (ACF not complete theory, because $\mathbb C \models \ACF$ and $\mathbb F_p^\alg \models \ACF$, but the $\mathscr L_\ring$-sentence $\myunder{1+\ldots + 1}{p\text{ times}}=0$ is not satisfied by $\mathbb C$ but satisfied by $\mathbb F_p^\alg$). More explicitly: adding the characteristic $p$ sentence produces a complete theory.
Compare with the ordinary way:
This also helps determine completions of ACF (ACF not complete theory, because $\mathbb C \models \ACF$ and $\mathbb F_p^\alg \models \ACF$, but the $\mathscr L_\ring$-sentence $\underbracket[0.2pt]{1+\ldots + 1}_{\scriptscriptstyle p\text{ times}}=0$ is not satisfied by $\mathbb C$ but satisfied by $\mathbb F_p^\alg$). More explicitly: adding the characteristic $p$ sentence produces a complete theory.
\end{document}