  <i>H</i> is the theory extending &#946;-conversion by identifying all closed
unsolvables. <i>H</i>&#969; is the closure of this theory under the &#969;-rule
(and &#946;-conversion). A long-standing conjecture of H. Barendregt states
that the provable equations of <i>H</i>&#969; form
&#928;<sub>1</sub><sup>1</sup>-complete set. Here we prove that conjecture.

Logic in Computer Science