Primitive recursive arithmetic plus transfinite induction up to (but not including) ε₀ — the first fixed point of α ↦ ω^α — proves the consistency of Peano arithmetic. Gentzen 1936. Aligns with Gödel's 2nd incompleteness: ε₀-induction is…
Primitive recursive arithmetic plus transfinite induction up to (but not including) ε₀ — the first fixed point of α ↦ ω^α — proves the consistency of Peano arithmetic. Gentzen 1936. Aligns with Gödel's 2nd incompleteness: ε₀-induction is…