Busy beaver machines with axiom-free Coq proofs: BB(7) σ > 3↑²⁰3, BB(8) > f_ω³(12), BB(9) > f_ω⁷(12), BB(10) f_(ω+1), BB(12) f_(ω+1)², BB(13)/BB(14) f_(ω+2), BB(4,3). Plus Turing machines that halt iff ZF/ZFC (253 states), ZFC + universes (296) or PA (238) is inconsistent.
☆12Oct 23, 2026Updated this week
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