We consider Borel sets of the form A ! (with usual topology) where cardinality of is less than some uncountable regular cardinal . We obtain a \normal form" of A, by nding a Borel set ( ) such that A and ( ) continuously reduce to each other. We do so by de ning Borel operations which are homomorphic to the rst Veblen ordinal functions of base required to compute the Wadge degree of the set A: the ordinal .I starts and plays letters in 33 II plays letters in T A ( T denotes the alphabet of the Tree T and A is the set of arrows of di erent type involved by operation )

We retrospectively reviewed 56 patients (71 hips) treated by total replacement for severe disability after pelvic irradiation. Symptoms were associated with various radiological lesions due to irradiation, including atraumatic femoral-neck fracture, osteonecrosis of the femoral head or of the acetabulum, and radiation osteitis of the whole pelvis. From 1970 to 1982 we used standard cemented components in 49 hips and had a high rate of acetabular loosening (52%) at a mean follow-up of 69 months. This was probably due to the mechanical insufficiency of irradiated periacetabular bone. From 1983 to 1990 we routinely used acetabular reinforcement rings. The rate of aseptic acetabular loosening in 22 hips at a mean follow-up of 40 months was 19%, but there were two septic loosenings emphasising the risk of infection in these patients. When total replacement is required for an irradiated hip, we recommend reinforcement of the acetabulum using a metallic ring, but there is still an increased risk of infection and in difficult cases such as severe acetabular destruction or soft-tissue or vascular injuries, a Girdlestone procedure may be indicated.

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