We develop a model of the untyped lambda calculus in non-wellfounded set theory. Every term is modeled by a set of pairs. This corresponds to how partial functions are normally represented in set theory. We show that modeling the untyped lambda calculus terms by total functions, or omitting mentioning the undefined term(s) causes the model to collapse to triviality.
This model of the lambda calculus is simple and intuitive, while capturing the recent approaches to modeling recursive domains.
By: Tom Costello
Published in: RJ10271 in 2002
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