What was already known
Hechler supplied the CH negative direction. Lee’s earlier positive result used a real-valued-measurable-cardinal or full-measure-extension hypothesis; the closed-set second question was already solved.
AI involvement
Glazer chose the problem and forcing route. The disclosure credits GPT-5.6 Sol with the central transfer argument and Claude models with Lean code under his direction; no independent human peer review is reported.
Sol supplied the central transfer argument within Glazer's human-directed set-theoretic program; Claude supplied the formal code.
- Supporting source (palomar-registry.org) — Assigned registry version and source pointer
Importance
Removes the large-cardinal assumption from the positive direction of a set-theory problem.
Limitations
The Lean project proves the positive model through a c⁺-coordinate random algebra, distinct from the paper’s ω₂-random-reals-over-CH route. Hechler’s negative direction and the closed-set question are earlier human results.
Technical verification
The cited status reports kernel-checked positive-model, independence and sentence-faithfulness targets with standard axioms and two Comparator configurations. The machine proof verifies the result through a changed random-forcing route, not the draft's literal omega_2-over-CH proof. This is source-reported, not reproduced here.
Independent checking
Pinned Lean build without sorry, standard-axiom audit, and both Mathlib-only and Flypitch Comparator challenges
- Checker
- Lean kernel and Comparator in Glazer's pinned repository
- Scope
- Positive ZFC model for Erdős 501's first question, independence targets and first-order sentence-faithfulness bridge
- Basis
- Reported by the linked checker
Human understanding
Default for missing evidence: Glazer chose the route and reviewed mathematics, but a human explanation of the core transfer and complete understanding of its mechanism is not documented.
Correction and publication history
Removes the large-cardinal assumption from the positive direction of a set-theory problem.
Read this published revision