Ideas from 'Principles of Arithmetic, by a new method' by Giuseppe Peano [1889], by Theme Structure

[found in 'From Frege to Gödel 1879-1931' (ed/tr Heijenoort,Jean van) [Harvard 1967,0-674-32449-8]].

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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA concerns any entities which satisfy the axioms [Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Russell]
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell]