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Typed lambda-calculus in classical Zermelo-Fraenkel set theory. (English) Zbl 0990.03008
In this paper the author introduces “$$\text{ZF}_\varepsilon$$ set theory” which, he claims, includes all of ZF + AF. However, his proof of the substitutivity for equality is not complete, so it is not clear whether his claim is justified. He then develops $$\text{ZF}_\varepsilon$$ set theory within a classical extension of lambda calculus.

##### MSC:
 03B40 Combinatory logic and lambda calculus 03E40 Other aspects of forcing and Boolean-valued models 68N18 Functional programming and lambda calculus
##### Keywords:
lambda calculus; set theory
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