diff --git a/kaplansky_direct_finite_char2_v2.txt b/kaplansky_direct_finite_char2_v2.txt
index 1084d4b..0d5bfb7 100644
--- a/kaplansky_direct_finite_char2_v2.txt
+++ b/kaplansky_direct_finite_char2_v2.txt
@@ -340,7 +340,7 @@ n >= 1. Put d_0 = (q - 2) / 2. Let S be the "index simplex"
 where a_0, a_1, ..., a_{q-1} is the chosen enumeration of Q. Let
 N_pt = q^n. Let l be an odd prime, D = l + 1. Suppose O is a subset
 of S and F is a family of full affine Q-lines contained in
-V = A \ O, with
+V = A minus O, with
 
       (i)   2 N_pt / D^2 <= |O| <= 7 N_pt / D^2;
       (ii)  every point of V lies on D members of F;
@@ -365,7 +365,7 @@ sufficiently large h >= 2, for every finite field Q of order q = 2^h
 and every enumeration of Q, there exist:
 
   - a set O subset S (S as in Proposition 3.3) of "holes", and
-  - a set F of full affine Q-lines, contained in V = A \ O,
+  - a set F of full affine Q-lines, contained in V = A minus O,
 
 such that
 
@@ -423,7 +423,7 @@ elements, K a finite extension of Q containing a primitive l-th root
 of unity zeta, and A = Q^n for n = 10b with b = s + 20 and
 s = floor(log_q D) where D = l + 1. Theorem 4.1 supplies a set
 O subset S (S = index simplex) of "holes" and a family F of
-full affine Q-lines in V = A \ O such that every point of V lies
+full affine Q-lines in V = A minus O such that every point of V lies
 on exact D lines of F, and the incidence graph has girth >= 12.
 
 Step 2. Produce the vectors x_v. Proposition 3.3 uses interpolation
@@ -1192,7 +1192,7 @@ Proposition (the pairing supplied by holes). Let q >= 4 be a power of
 two, Q a field of order q, fix an enumeration of Q, let n >= 1, and
 put d_0 = (q - 2) / 2, S = S_{d_0} subset A = Q^n, N_pt = q^n. Let l
 be an odd prime and D = l + 1. Suppose that O subset S and that F is
-a family of full affine Q-lines contained in V = A \ O, with
+a family of full affine Q-lines contained in V = A minus O, with
 
       2 N_pt / D^2 <= |O| <= 7 N_pt / D^2,                       (hole size)
 
@@ -1227,7 +1227,7 @@ affine Q-lines with exactly q points.
 
 Theorem (hypergraph). For all sufficiently large h, for every Q and
 enumeration as above, there are a set O subset S and a set F of
-affine lines contained in V = A \ O such that
+affine lines contained in V = A minus O such that
 
       2 N_pt / D^2 <= |O| <= 7 N_pt / D^2,
       every point of V lies on exactly D members of F,