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- W2124870057 abstract "Abstract We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some familiar results in the theory of (complete) Boolean algebras—notably, the proposition that every complete Boolean algebra is an absolute subretract. This (almost) resolves a question of Banaschewski and Bhutani as to whether the Sikorski extension theorem for Boolean algebras is persistent." @default.
- W2124870057 created "2016-06-24" @default.
- W2124870057 creator A5046508035 @default.
- W2124870057 date "1997-12-01" @default.
- W2124870057 modified "2023-10-16" @default.
- W2124870057 title "Zorn's lemma and complete Boolean algebras in intuitionistic type theories" @default.
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- W2124870057 doi "https://doi.org/10.2307/2275642" @default.
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