diff --git a/planar_xy_spin_field_v2.txt b/planar_xy_spin_field_v2.txt
index 2764805..24da39f 100644
--- a/planar_xy_spin_field_v2.txt
+++ b/planar_xy_spin_field_v2.txt
@@ -19,7 +19,7 @@ Let D = (-1,1)^2 be the open unit square. For n >= 1 put
    E_n      = { {x,y} : x,y in D_n, |x-y| = 1/n }.
 
 An angle theta_x in R/(2 pi Z) sits at each x in D_n. Boundary
-angles, i.e. those with x in D_n \ D_n^o, are fixed to 0.
+angles, i.e. those with x in D_n minus D_n^o, are fixed to 0.
 
 For b > 0 the fixed-boundary (pinned) spin law is
 
@@ -88,8 +88,8 @@ as n -> infinity the distributions S_n converge in law to V_* in
 H^{-3}_loc(D). Moreover, for every k >= 1, every f_1,...,f_k in
 C_c^inf(D;C), and all nonnegative integers p_j, q_j,
 
-   E_n^0 prod_j S_n(f_j)^{p_j} \overline{S_n(f_j)}^{q_j}
-      -> E prod_j V_*(f_j)^{p_j} \overline{V_*(f_j)}^{q_j}.
+   E_n^0 prod_j S_n(f_j)^{p_j} conj(S_n(f_j))^{q_j}
+      -> E prod_j V_*(f_j)^{p_j} conj(V_*(f_j))^{q_j}.
 
 The joint laws of the complex smeared fields also converge.
 
@@ -804,10 +804,10 @@ symmetric in the four quadrants). All side lengths and passages are
 nondegenerate. Write Q_r = (-r,r)^2, choose lambda a sufficiently
 large power of 4, and put
 
-   A_lambda = lambda P \ (P)^o,
-   p        = closure(Q_{2 sqrt lambda}) \ Q_{sqrt lambda},
+   A_lambda = lambda P minus (P)^o,
+   p        = closure(Q_{2 sqrt lambda}) minus Q_{sqrt lambda},
    H_in     = A_lambda and closure(Q_4),
-   H_out    = A_lambda \ Q_{lambda/4}.
+   H_out    = A_lambda minus Q_{lambda/4}.
 
 Sobolev spaces on A_lambda refer to its interior. The guard p is a
 full square band separating the two ends; each end region contains
@@ -1085,7 +1085,7 @@ function; integration on concentric circles proves the matching
 lower bound. Restriction of admissible forms, with
 B(0,1-eps) subset P subset B(0,1+eps), gives
 
-   M(lambda P \ P^o) = 2 pi log lambda + O(eps),
+   M(lambda P minus P^o) = 2 pi log lambda + O(eps),
 
 constant independent of large lambda: the circular annulus with
 radii 1+eps and lambda(1-eps) is contained in the polygonal one,
@@ -1093,7 +1093,7 @@ which is contained in the circular annulus with radii 1-eps and
 lambda(1+eps). The same bounds with lambda^2 hold for the union of
 two blocks, so
 
-   0 <= M(lambda^2 P \ P^o) - 2 M(lambda P \ P^o) <= C eps
+   0 <= M(lambda^2 P minus P^o) - 2 M(lambda P minus P^o) <= C eps
 
 (the lower bound by restriction to the two cut annuli, whose
 energies agree by scale invariance in dimension two). Theorem 5.1,
@@ -1249,7 +1249,7 @@ the L^2 norm of v . nu on such a circle is O(rho^{1/2}), while trace
 and Poincare on the adjacent annulus of radii rho and 2 rho give
 
    |g - circle mean|_{L^2(dB(z_i,rho))}
-     <= C rho^{1/2} |nabla g|_{L^2(B(z_i,2rho)\B(z_i,rho))},
+     <= C rho^{1/2} |nabla g|_{L^2(B(z_i,2rho) minus B(z_i,rho))},
 
 collars disjoint. So minimizing |v + nabla g|_2^2 changes |v|_2^2 by
 at most O(rho^2). Compute |v|_2^2 = (2 pi)^2 integral |nabla U|^2.