diff --git a/semialgebraic_universal_covers_v2.txt b/semialgebraic_universal_covers_v2.txt
index 278bf3c..4e46c73 100644
--- a/semialgebraic_universal_covers_v2.txt
+++ b/semialgebraic_universal_covers_v2.txt
@@ -674,7 +674,7 @@ the statement is exactly:
   center x_1, let L be the smooth projective model of its plaque
   (as in 3.4.1). Then there is a symmetric meromorphic matrix H on
   L, holomorphic near the original plaque, such that Im H > 0 there,
-  and the weighted tangent inequality is
+  and the weighted tangent ineuality is
 
     q_z(s, w)  =  Im s  -  (Im w)^T  (Im H(z))^{-1}  (Im w)  >  0
                                                             for
@@ -691,12 +691,12 @@ the recursive induction of 3.4.5, the second block will itself be
 described recursively; so the tower has a "stack" of (s_j, w_j)
 blocks indexed by j = 1, 2, ..., k.
 
-Quadratic test on the first block. The inequality defining the V-side
+Quadratic test on the first block. The ineuality defining the V-side
 near the plaque is
 
   Im s  >  (Im w)^T (Im H(z))^{-1} (Im w),
 
-with the reverse inequality defining the complement side. Because
+with the reverse ineuality defining the complement side. Because
 Im H(z) > 0, the right side is a strictly convex quadratic function of
 Im w with minimum 0 at Im w = 0. The solution set is a convex
 horizontal "paraboloid" region in (s, w) above the plaque-z, and it
@@ -852,7 +852,7 @@ The main proposition is:
          L, of complex dimension ell < dim Y.
 
     (ii) Over every y in V_2, every point (s, w) in C x C^r satisfying
-         the strict inequality
+         the strict ineuality
 
               Im s  >  (Im w)^T (Im H(y))^{-1} (Im w)
 
@@ -1070,7 +1070,7 @@ The domain P is a "triangular" domain, with the "later" stages
 constrained by the "earlier" ones only through the off-diagonal of
 the Hermitian matrix tau_j.
 
-Why this is a bounded domain. Each stage j's inequality is
+Why this is a bounded domain. Each stage j's ineuality is
 
   Im s_j  >  (Im w_j)^T (Im tau_j(z_j))^{-1} (Im w_j).
 
@@ -1144,7 +1144,7 @@ later:
 Proof of (a): P is diffeomorphic to R^{2d}.
 
 At one stage of the tower, write B(z) := Im tau_j(z_{>j}).
-The defining inequality of stage j is Im M_j > 0, i.e. in Schur
+The defining ineuality of stage j is Im M_j > 0, i.e. in Schur
 complement form
 
   Im s_j  >  (Im w_j)^T B(z_{>j})^{-1} (Im w_j).
@@ -1737,7 +1737,7 @@ holomorphic functions.
   of strictly positive harmonic functions with h(o) = 1 for a
   fixed point o.
 
-  - (Compactness of H). Local Harnack inequalities (Serrin 1964,
+  - (Compactness of H). Local Harnack ineualities (Serrin 1964,
     Theorems 5-7) plus interior elliptic estimates (Nirenberg 1959)
     make H compact in the C^inf topology on compact subsets. Limits
     are still strictly positive: they are nonnegative harmonic functions
@@ -2588,7 +2588,7 @@ precise role each plays.
       Hilbert transform boundedness on L^q.
 
     - Serrin 1964, Acta. Math.
-      Local Harnack inequalities.
+      Local Harnack ineualities.
 
     - Nirenberg 1959, Ann. SNS Pisa.
       Interior elliptic estimates.