Journal of Symbolic Logic 62 (4):1265-1279 (1997)

John L. Bell
University of Western Ontario
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
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DOI 10.2307/2275642
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References found in this work BETA

Lectures on Boolean Algebras.Paul R. Halmos - 1966 - Journal of Symbolic Logic 31 (2):253-254.
Toposes and Local Set Theories. An Introduction.J. L. Bell - 1990 - Journal of Symbolic Logic 55 (2):886-887.

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Citations of this work BETA

Formal Zariski Topology: Positivity and Points.Peter Schuster - 2006 - Annals of Pure and Applied Logic 137 (1-3):317-359.
Countable Choice as a Questionable Uniformity Principle.Peter M. Schuster - 2004 - Philosophia Mathematica 12 (2):106-134.
Boolean Algebras and Distributive Lattices Treated Constructively.John L. Bell - 1999 - Mathematical Logic Quarterly 45 (1):135-143.
Some New Intuitionistic Equivalents of Zorn’s Lemma.John L. Bell - 2003 - Archive for Mathematical Logic 42 (8):811-814.
Some Forms of Excluded Middle for Linear Orders.Peter Schuster & Daniel Wessel - 2019 - Mathematical Logic Quarterly 65 (1):105-107.

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