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3 ideas

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

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The compactness theorem can prove nonstandard models of PA [Halbach]

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The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

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To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]