如何解决 LaTeX 中的段落对齐问题

Question 1

感谢您发布可编译的 MWE，因为它极大地简化了对格式化目标解决方案的搜索，即如何修复涉及内联数学对象的错误换行情况。

以下屏幕截图中的第一个推论复制了 OP 的屏幕截图。
在为原作者的既定目标提供解决方案之前，有必要对相关段落进行一些小修改。例如，值得替换
```
 $\,\widetilde{\phi_i}\,=\underset{N_i<n_i<\omega}
 {\displaystyle\bigwedge}{\phi}_{n_i}$ 
```
和
```
 $\widetilde{\phi}_i=
 \smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
```
以避免在推论的最后一行的“大楔形”符号周围产生巨大且难看的视觉间隙。（该宏\smashoperator由数学工具包，它是数学包。）此外，由于\mathfrak只对大写字母进行操作，因此最好写成\mathfrak{M}_i而不是\mathfrak{M_i}。请参阅下面的第二个推论，了解修复这些初步问题的结果。
正如 @barbarabeeton 在评论中指出的那样，有两种方法可以解决 OP 遇到的格式问题。第一种方法是手动\allowbreak在有问题的内联数学公式中的某个位置插入一个指令（具体来说，是指令），以指示应该在哪里换行。在这里，允许在之后换行似乎是一个好主意\colon。请参阅下面的第三个推论。
第二种解决方案是切换到显示公式；请参阅下面的第四个推论。我认为这是迄今为止大多数此类用例的最佳解决方案。

\documentclass[11pt,twoside]{article}
\usepackage{amssymb}
\usepackage{mathtools} % 'mathtools' is a superset of 'amsmath'
%\usepackage{amsfonts} % 'amsfonts' is loaded automatically by 'amssymb'

\usepackage{geometry}
\geometry{hmargin=1in,vmargin=1.25in}
% '{margin=1in,top=1.25in,bottom=1.25in}' isn't unambiguous

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\begin{document}

\setcounter{section}{2}
\setcounter{theorem}{5} % just for this example

\begin{corollary}   \label{16}
\ Suppose in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of a $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi_i}$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M_i}}$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M_i}}\models\widetilde{\phi_i}$. 
In addition, there is a $N_i\in\omega$ such that
$\,\widetilde{\phi_i}\,=\underset{N_i<n_i<\omega}
{\displaystyle\bigwedge}{\phi}_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M_i}}$. 
\end{corollary}

\begin{corollary}   \label{16a}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\begin{corollary}   \label{16b}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon \allowbreak % <-- '\allowbreak' is new
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\begin{corollary}   \label{16c}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
\[
\bigl\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\bigr\} \,.
\] 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\end{document}

Answer

感谢您发布可编译的 MWE，因为它极大地简化了对格式化目标解决方案的搜索，即如何修复涉及内联数学对象的错误换行情况。

以下屏幕截图中的第一个推论复制了 OP 的屏幕截图。
在为原作者的既定目标提供解决方案之前，有必要对相关段落进行一些小修改。例如，值得替换
```
 $\,\widetilde{\phi_i}\,=\underset{N_i<n_i<\omega}
 {\displaystyle\bigwedge}{\phi}_{n_i}$ 
```
和
```
 $\widetilde{\phi}_i=
 \smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
```
以避免在推论的最后一行的“大楔形”符号周围产生巨大且难看的视觉间隙。（该宏\smashoperator由数学工具包，它是数学包。）此外，由于\mathfrak只对大写字母进行操作，因此最好写成\mathfrak{M}_i而不是\mathfrak{M_i}。请参阅下面的第二个推论，了解修复这些初步问题的结果。
正如 @barbarabeeton 在评论中指出的那样，有两种方法可以解决 OP 遇到的格式问题。第一种方法是手动\allowbreak在有问题的内联数学公式中的某个位置插入一个指令（具体来说，是指令），以指示应该在哪里换行。在这里，允许在之后换行似乎是一个好主意\colon。请参阅下面的第三个推论。
第二种解决方案是切换到显示公式；请参阅下面的第四个推论。我认为这是迄今为止大多数此类用例的最佳解决方案。

\documentclass[11pt,twoside]{article}
\usepackage{amssymb}
\usepackage{mathtools} % 'mathtools' is a superset of 'amsmath'
%\usepackage{amsfonts} % 'amsfonts' is loaded automatically by 'amssymb'

\usepackage{geometry}
\geometry{hmargin=1in,vmargin=1.25in}
% '{margin=1in,top=1.25in,bottom=1.25in}' isn't unambiguous

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\begin{document}

\setcounter{section}{2}
\setcounter{theorem}{5} % just for this example

\begin{corollary}   \label{16}
\ Suppose in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of a $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi_i}$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M_i}}$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M_i}}\models\widetilde{\phi_i}$. 
In addition, there is a $N_i\in\omega$ such that
$\,\widetilde{\phi_i}\,=\underset{N_i<n_i<\omega}
{\displaystyle\bigwedge}{\phi}_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M_i}}$. 
\end{corollary}

\begin{corollary}   \label{16a}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\begin{corollary}   \label{16b}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
$\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon \allowbreak % <-- '\allowbreak' is new
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\begin{corollary}   \label{16c}
Suppose that in a sequence of structures
$\{(\mathfrak{M}_{n},\phi_n)\colon 
\mathfrak{M}_{n} \models\phi_{n}\land n<\omega\}$ 
of an $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures
\[
\bigl\{(\mathfrak{M}_{n_i}, \phi_{n_i}) \colon 
\mathfrak{M}_{n_i} \models\phi_{n_i}\land n_i<\omega\bigr\} \,.
\] 
Then there is a unique formula
$\widetilde{\phi}_i$ in $\mathcal{L}$ (up to 
equivalence) and a unique countable atomic structure 
$\widetilde{\mathfrak{M}}_i$ (up to isomorphism) for each 
$\{(\mathfrak{M}_{n_i},\phi_{n_i})\}$ such that
$\widetilde{\mathfrak{M}}_i\models\widetilde{\phi}_i$. 
In addition, there is an $N_i\in\omega$ such that
$\widetilde{\phi}_i=
\smashoperator{\bigwedge_{N_i<n_i<\omega}} \phi_{n_i}$ 
which is the complete formula of
$\widetilde{\mathfrak{M}}_i$. 
\end{corollary}

\end{document}

Question 2

我认为你不应该\colon在这种情况下使用，它用于像中的地图f\colon A\rightarrow B。在集合构建器符号中，冒号是关系符号。

您还应该使用更好的名称，例如\fMfor\mathfrak{M}和\cLfor \mathcal{L}，这使得输入更简单，并避免诸如这样的错误\mathfrak{M_i}，而应该是\mathfrak{M}_i。

我还使用了直立括号（我不太喜欢它们在 Computer Modern 中的倾斜）。

\models最后，我用替换了的丑陋实现\vDash。

\documentclass[11pt,twoside]{article}%
\usepackage{geometry}
\usepackage{amssymb}
\usepackage{amsmath}

\geometry{margin=1in,top=1.25in,bottom=1.25in}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\newcommand{\fM}{\mathfrak{M}}
\newcommand{\cL}{\mathcal{L}}
\newcommand{\wt}{\widetilde}

\renewcommand{\models}{\vDash}

\begin{document}

\begin{corollary}\label{16}
Suppose in a sequence of structures
$\{(\fM_{n},\phi_n): \fM_{n} \models \phi_{n}\land n<\omega\}$
of a  $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures 
$\{(\fM_{n_i}, \phi_{n_i}) : \fM_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula $\wt{\phi_i}$ in $\cL$ 
\textup{(}up to equivalence\textup{)} and a unique countable atomic structure 
$\wt{\fM_i}$ \textup{(}up to isomorphism\textup{)} for each  
$\{(\fM_{n_i},\phi_{n_i})\}$ such that
$\wt{\fM_i}\models\wt{\phi_i}$.
In addition, there is a $N_i\in\omega$ such that
$\wt{\phi_i}\,= \bigwedge_{N_i<n_i<\omega}\phi_{n_i}$ 
which is the complete formula of $\wt{\fM_i}$. 
\end{corollary}

\end{document}

\underset最后一个大公式是错误的。你可能使用

\bigwedge\limits_{N_i<n_i<\omega}\phi_{n_i}

对于构造位于推论的最后一行但在内联的特殊情况，最好在侧面设置限制。

如果你确实想使用\colon间距，请定义自己的允许换行的符号

\documentclass[11pt,twoside]{article}%
\usepackage{geometry}
\usepackage{amssymb}
\usepackage{amsmath}

\geometry{margin=1in,top=1.25in,bottom=1.25in}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\newcommand{\fM}{\mathfrak{M}}
\newcommand{\cL}{\mathcal{L}}
\newcommand{\wt}{\widetilde}

\renewcommand{\models}{\vDash}

\newcommand{\suchthat}{\colon\allowbreak}

\begin{document}

\begin{corollary}\label{16}
Suppose in a sequence of structures
$\{(\fM_{n},\phi_n)\suchthat \fM_{n} \models \phi_{n}\land n<\omega\}$
of a  $\aleph_{0}$-categorical theory $T$, there are 
finitely many homogeneous subsequences of structures 
$\{(\fM_{n_i}, \phi_{n_i}) \suchthat \fM_{n_i} \models\phi_{n_i}\land n_i<\omega\}$. 
Then there is a unique formula $\wt{\phi_i}$ in $\cL$ 
\textup{(}up to equivalence\textup{)} and a unique countable atomic structure 
$\wt{\fM_i}$ \textup{(}up to isomorphism\textup{)} for each  
$\{(\fM_{n_i},\phi_{n_i})\}$ such that
$\wt{\fM_i}\models\wt{\phi_i}$.
In addition, there is a $N_i\in\omega$ such that
$\wt{\phi_i}\,= \bigwedge_{N_i<n_i<\omega}\phi_{n_i}$ 
which is the complete formula of $\wt{\fM_i}$. 
\end{corollary}

\end{document}

Answer