Rocq formalization shows Peano Arithmetic proves "K230 halts iff NOT Con(ZFC)"
burny_tech · x · 2026-10-24
Elliot Glazer updated his repo with a classical Rocq verification that Peano Arithmetic proves "K230 halts iff NOT Con(ZFC)" — a purely existential claim, and extracting an actual PA proof from it will take substantial compute.
Peter Scholze amplified it, noting this is something he's wanted to see for years: a claim requiring two levels of metatheory — "CiC believes [PA believes [some claim]]". Normally the metametatheory drops out by elaborating the metatheory proof, but here Elliot's metametatheory proof is essentially non-constructive. Nobody doubts PA directly proves the claim, but it remains a fun demonstration.
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