Cleaned up notations for logic.

src/logic/notation.tex

@@ -6,6 +6,8 @@
     \hline
     % ---- Topological Vector Spaces ----
     $\mathcal{L} = (\mathcal{F}, \mathcal{R}, \mathcal{C})$ & Language $\mathcal{L}$ with function symbols $\mathcal{F}$, relation symbols $\mathcal{R}$, and constant symbols $\mathcal{C}$. & \autoref{definition:language} \\
-    $\mathcal{M} = (M, f^\cm, R^\cm, c^\cm)$ & $\mathcal{L}$-structure with functions $\bracsn{f^\cm|f \in \mathcal{F}}$, relations $\bracsn{R^\cm|R \in \mathcal{R}}$, and constants $\bracsn{c^\cm|c \in \mathcal{C}}$. & \autoref{definition:language-structure}
+    $\mathcal{M} = (M, f^\cm, R^\cm, c^\cm)$ & $\mathcal{L}$-structure with functions $\bracsn{f^\cm|f \in \mathcal{F}}$, relations $\bracsn{R^\cm|R \in \mathcal{R}}$, and constants $\bracsn{c^\cm|c \in \mathcal{C}}$. & \autoref{definition:language-structure} \\
+    $\mathcal{T}(\mathcal{L})$ & Set of $\mathcal{L}$-terms. & \autoref{definition:logic-terms} \\
+    $\mathcal{T}_n(\mathcal{L})$ & Set of $\mathcal{L}$-terms of complexity at most $n$. & \autoref{lemma:logic-terms-induction}
 \end{tabular}
 

src/logic/tp/lang.tex

@@ -47,7 +47,7 @@
     \mathcal{T}_{n}(\mathcal{L}) = \mathcal{T}_{n-1}(\mathcal{L}) \cup \bracsn{f(t_1, \cdots, t_{n_f})|f \in \mathcal{F}, \bracsn{t_j}_1^{n_f} \in \mathcal{T}_{n-1}(\mathcal{L})}
     \]
 
-    then $\mathcal{T} = \bigcup_{n \in \natz}\mathcal{T}_n$. For each $n \in \natz$, $\mathcal{T}_n$ is the set of \textbf{$\mathcal{L}$-terms of complexity at most $n$}.
+    then $\mathcal{T}(\mathcal{L}) = \bigcup_{n \in \natz}\mathcal{T}_n(\mathcal{L})$. For each $n \in \natz$, $\mathcal{T}_n$ is the set of \textbf{$\mathcal{L}$-terms of complexity at most $n$}.
 \end{lemma}