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Ideas of Giuseppe Peano, by Text

[Italian, 1858 - 1932, Professor at Turin.]

1889 Principles of Arithmetic, by a new method
1.2 p.3 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach]
11 p.48 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R]
6.3 p.183 PA concerns any entities which satisfy the axioms [Bostock]
p.276 p.276 Peano axioms not only support arithmetic, but are also fairly obvious [Russell]
p.276 p.276 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell]
1890 works
p.245 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Flew]
p.279 Numbers have been defined in terms of 'successors' to the concept of 'zero' [Blackburn]