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'On the Question of Absolute Undecidability', 'Intensions Revisited' and 'Philosophies of Mathematics'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
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17899
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Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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10128
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The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman]
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17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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17902
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A successor is the union of a set with its singleton [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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10133
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Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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10130
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Set theory can prove the Peano Postulates [George/Velleman]
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