(I'm throwing a new thread because this is different from Ken Kubota's thoughts.)
"Hence (1 <https://plato.stanford.edu/entries/logic-higher-order/#mjx-eqn-ind>1) [Induction axiom] cannot be expressed in first order logic. " (1) So there are 5 axioms in the axiomatic system of natural numbers. Four of them can be expressed in FOL. The fifth one [Induction axiom] can only be expressed in second-order logic. I don't know if there is an official acronym for second-order logic but let's call it SOL. And let's call PEANO the system of 5 axioms designed by Peano (1) https://plato.stanford.edu/entries/logic-higher-order/ A Peano system is necessarily equal to SOL + PEANO. FOL + PEANO is impossible. -- FL -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/68a5f815-8dbd-47d7-99fc-e9678388b33d%40googlegroups.com.
