Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'The Rationalists' and 'Set Theory and Its Philosophy'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

10712

If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

There are at least eleven types of large cardinal, of increasing logical strength [Koellner]

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

17882

It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]

17887

PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]