Ideas of Giuseppe Peano, by Theme
[Italian, 1858  1932, Professor at Turin.]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
3338

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

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949

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

18113

PA concerns any entities which satisfy the axioms [Bostock]

17634

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

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]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653

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

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635

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