On Henk Barendregt's Favorite Open Problem

Benedetto Intrigila
Università di Roma ”Tor Vergata”, Rome, Italy

Richard Statman
Carnegie-Mellon University, Pittsburgh, PA, USA


H is the lambda-theory extending beta-conversion by identifying all closed unsolvables. A long-standing open problem of H. Barendregt states that the range property holds in H. Here we discuss what we know about the problem. We also make some remarks on the lambda-theory H-omega (the closure of H under the omega-rule and beta-conversion).

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