diff --git a/II_L/logic_and_set_theory.tex b/II_L/logic_and_set_theory.tex
index 28bbf64..cde26d1 100644
--- a/II_L/logic_and_set_theory.tex
+++ b/II_L/logic_and_set_theory.tex
@@ -432,12 +432,12 @@ \subsection{Syntactic implication}
 \end{cor}
 
 \begin{thm}[Completeness theorem]\index{completeness theorem}
-  Le $S\subset L$ and $t\in L$. Then $S\models t$ if and only if $S\vdash t$.
+  Let $S\subset L$ and $t\in L$. Then $S\models t$ if and only if $S\vdash t$.
 \end{thm}
 
 This theorem has two nice consequences.
 \begin{cor}[Compactness theorem]\index{compactness theorem}
-  Let $S\subset L$ and $t\in L$ with $S\models t$. Then there is some finite $S'\subset S$ has $S'\models t$.
+  Let $S\subset L$ and $t\in L$ with $S\models t$. Then there is some finite $S'\subset S$ such that $S'\models t$.
 \end{cor}
 
 \begin{proof}