High Quality Content by WIKIPEDIA articles! In mathematics, Robinson arithmetic, or Q, is a finitely axiomatized fragment of Peano arithmetic (PA), first set out in Robinson (1950). Q is essentially PA without the axiom schema of induction. Since Q is weaker than PA, it is incomplete. The crucial importance of Q is that this finitely axiomatized fragment of PA is already recursively incompletable and essentially undecidable. Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number theory.

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