On the λY calculus

Annals of Pure and Applied Logic 130 (1-3):325-337 (2004)
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Abstract

The λY calculus is the simply typed λ calculus augmented with the fixed point operators. We show three results about λY: the word problem is undecidable, weak normalisability is decidable, and higher type fixed point operators are not definable from fixed point operators at smaller types

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Completeness, Invariance and Λ-Definability.R. Statman - 1982 - Journal of Symbolic Logic 47 (1):17-26.

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