Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Russell's Mathematical Logic' and 'talk'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

10046

The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]

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

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

10039

Some arithmetical problems require assumptions which transcend arithmetic [Gödel]

17891

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

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10043

Mathematical objects are as essential as physical objects are for perception [Gödel]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

10045

Impredicative definitions are admitted into ordinary mathematics [Gödel]