• Newberry
    5
    Let P_1, P_2, … P_7 be the Peano axioms. What will happen if we add

    P+: P1 & P2 & … P7 & ∃x(Prf(x, ⌜P⌝) → P

    Here ⌜P⌝ means the Gödel number of P, and Prf(x,y) means that x is a proof o y, or rather that x is the Gödel number of a sequence that is a proof a sentence with Gödel number y.
    It seems to me that the axiom is true. For if our derivation system is sound, and it derives P then it is the case that P.
  • alan1000
    181
    What are the 6th and 7th Dedekind/Peano axioms?
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