What is the best book to learn Peano Arithmetic

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My goal is to develop an automated proof program for Peano arithmetic. I want to know as much proofs as possible in this system for both my mathematical culture and to enrich the database of my future artificial intelligence.

I'm thinking of using Racket or Haskell.

Thank you in advance,

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I suggest:

  • Edmund Landau's Foundations of Analysis, chapter I;
  • Solomon Feferman's The number systems, chapter III.