Set Theory & Logic Codexery — Data & Quality

We publish our audit record because accuracy claims should be checkable. Every entry on this site runs through an automated fact-audit pipeline (accuracy audit → source-grounded repair → visual QA); this page is generated from that pipeline's own report, not written by hand.

Last full accuracy audit: 2026-09-05 · 19 entries checked · 4 flagged · 6 issues confirmed · 0 corrected · 6 still open

Recent findings (audit lane, verbatim)

Partition of a set — The empty set has exactly one partition, which is the empty collection of subsets, not the empty set itself.

Partition of a set — In type theory and proof theory, a setoid is a set equipped with an equivalence relation, not a partition; calling a partition a setoid is not standard canon.

Principle of explosion — The claim that the principle of explosion was first proved by the 12th-century French philosopher William of Soissons is not supported by established historical canon.

Quantifier elimination — The entry claims 'Skolem arithmetic' is a theory shown decidable using quantifier elimination, but Skolem arithmetic is not typically decidable via standard quantifier elimination; it is decidable by other means, so listing it as a classic example is misleadin

Russell's paradox — The entry states that Russell published the paradox in 1901, but he actually discovered it in 1901 and published it in 1903 in The Principles of Mathematics.

Russell's paradox — The entry says 'Georg Cantor had also realized that his theory would lead to a contradiction, as he told David Hilbert and Richard Dedekind by letter.' This is an overstatement; Cantor identified a specific antinomy (the set of all cardinal numbers) but did no

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Corrections

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