Lifschitz realizability as a topological construction

Journal of Symbolic Logic 85 (4):1342-1375 (2020)
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Abstract

We develop a number of variants of Lifschitz realizability for $\mathbf {CZF}$ by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with variants of the lesser limited principle of omniscience including consistency with unique Church’s thesis, consistency with some Brouwerian principles and variants of the numerical existence property.

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2021-01-08

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Michael Rathjen
University of Leeds

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Heyting-valued interpretations for Constructive Set Theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
Basic subtoposes of the effective topos.Sori Lee & Jaap van Oosten - 2013 - Annals of Pure and Applied Logic 164 (9):866-883.

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