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Solution of a Problem of Barendregt on Sensible lambda-Theories

Benedetto Intrigila ; Richard Statman.

<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&nbsp;[&hellip;]

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On sets of terms having a given intersection type

Andrew Polonsky ; Richard Statman.

Working in a variant of the intersection type assignment system of Coppo, Dezani-Ciancaglini and Venneri [1981], we prove several facts about sets of terms having a given intersection type. Our main result is that every strongly normalizing term M admits a *uniqueness typing*, which is a pair&nbsp;[&hellip;]

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