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'fragments/reports', 'Foundations without Foundationalism' and 'Intermediate Logic'
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4 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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13657
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First-order arithmetic can't even represent basic number theory [Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
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13358
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Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock]
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13359
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Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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13656
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Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro]
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