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The axioms of Peano Arithmetic
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Abstract
The quotations at the head of this chapter is how Peano stated his famous five axioms of arithmetic. (His notation looks surprisingly modern. In particular his use of ⊃) for implication and set-inclusion has become the modern-day ⊃i and ⊃, , although the ‘subset’ relation symbol ⊃) is now written the other way round, as ⊆ !) Essentially, Peano’s axioms are those of PA− together with the second-order induction axiom where X ranges over all subsets of the domain of the stucture under consideration, and x, y range over elements of this domain.
Title: The axioms of Peano Arithmetic
Description:
Abstract
The quotations at the head of this chapter is how Peano stated his famous five axioms of arithmetic.
(His notation looks surprisingly modern.
In particular his use of ⊃) for implication and set-inclusion has become the modern-day ⊃i and ⊃, , although the ‘subset’ relation symbol ⊃) is now written the other way round, as ⊆ !) Essentially, Peano’s axioms are those of PA− together with the second-order induction axiom where X ranges over all subsets of the domain of the stucture under consideration, and x, y range over elements of this domain.
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