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LIT-390: Topos Theory and Consistent Histories: The Internal Logic of the Set of All Consistent Sets

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Properties5
StatusActive — read in full 2026-10-01 (NOTE-333); worth reading as the origin of the Isham school's sieve-valued, coarse-graining truth values, which the Kochen–Specker series names as its motivation (KS I, ref. [13]); it is the only place the construction is applied to consistent histories, it is short and elementary, and its constructions are correct as stated, but read it knowing that the Heyting values measure only whether α can be embedded in a consistent set (the probability d(α, α) is the same in every window), so it says nothing about the conflicts between consistent sets that motivate it.
Version2
Tagsquantum-foundations, logic, contextuality, mathematics, philosophy-of-science
Cited as “paper” byNOTE-333 — Topos Theory and Consistent Histories: The Internal Logic of the Set of All Consistent Sets
Cited as “source” byTHEORY-024 — Classical Boolean logic is restored when a presheaf of contextual data acquires a global section or is sheafified

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Isham (1996), International Journal of Theoretical Physics 36(4), 785–814 (April 1997); title, author, volume, issue and pages confirmed against Crossref and arXiv — arXiv:gr-qc/9607069

Standing in the record

Filed on 2026-10-01 at the owner’s request. published: is the first appearance (ADR-002).

It was filed Deferred, unread. NOTE-333 is the close reading of 2026-10-01, and it placed the work: Active — worth reading as the origin of the Isham school’s sieve-valued, coarse-graining truth values, which the Kochen–Specker series names as its motivation (KS I, ref. [13]); it is the only place the construction is applied to consistent histories, it is short and elementary, and its constructions are correct as stated, but read it knowing that the Heyting values measure only whether α can be embedded in a consistent set (the probability d(α, α) is the same in every window), so it says nothing about the conflicts between consistent sets that motivate it.

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