Realizing Realizability Results with Classical Constructions

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Abstract

J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e. symmetric extensions. We also provide a new condition for preserving well-ordered, and other particular type of choice, in the general settings of symmetric extensions.
Original languageEnglish
Pages (from-to)429-445
Number of pages17
JournalBulletin of Symbolic Logic
Volume25
Issue number4
Early online date19 Dec 2019
DOIs
Publication statusPublished - Dec 2019

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