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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157
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Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
13701
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A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]
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