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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

15653

We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach]

11

p.48

13949

All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R]

6.3

p.183

18113

PA concerns any entities which satisfy the axioms [Bostock]

p.276

p.276

17634

Peano axioms not only support arithmetic, but are also fairly obvious [Russell]

p.276

p.276

17635

Arithmetic can have even simpler logical premises than the Peano Axioms [Russell]


p.245

5897

0 is a nonsuccessor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(alln) [Flew]


p.279

3338

Numbers have been defined in terms of 'successors' to the concept of 'zero' [Blackburn]
