Solution of a Problem of Barendregt on Sensible lambda-Theories
<|reference_start|>Solution of a Problem of Barendregt on Sensible lambda-Theories: <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.<|reference_end|>
@article{intrigila2006solution,
    title={Solution of a Problem of Barendregt on Sensible lambda-Theories},
    author={Benedetto Intrigila and Richard Statman},
    journal={Logical Methods in Computer Science, Volume 2, Issue 4 (October
  18, 2006) lmcs:2241},
    year={2006},
    doi={10.2168/LMCS-2(4:5)2006},
    archivePrefix={arXiv},
    eprint={cs/0609080},
    primaryClass={cs.LO}
}