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'On the Question of Absolute Undecidability', 'On the Plurality of Worlds' and 'Investigations in the Foundations of Set Theory I'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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13487
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In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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17890
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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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 / g. Incompleteness of Arithmetic
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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 / f. Zermelo numbers
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18178
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For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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13027
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Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9627
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Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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