The conclusion of Gödel's second incompleteness theorem also holds for Q: no consistent recursively axiomatized extension of Q can prove its own consistency, even if we additionally restrict Gödel numbers of proofs to a definable cut.
The conclusion of Gödel's second incompleteness theorem also holds for Q. No consistent recursively axiomatized extension of Q can prove its own consistency. We additionally restrict Gödel numbers of proofs to a definable cut.