Mathematical logic and foundations Ordinals and cardinals Concept
Ordinal number
Summary
Ordinal numbers extend the natural numbers to measure the length of well-ordered sets, including infinite ones. Each well-ordered set is order isomorphic to exactly one ordinal.
Where this leads
26 pages build on this one.
- Long line
- Von Neumann universe
- Ordinal analysis
- Woodin cardinal
- Constructible universe
- Kunen's inconsistency theorem
- Ordinal analysis
- Proof-theoretic ordinal
- Burali-Forti paradox
- Tychonoff plank
- Ulm's theorem
- Axiom schema of replacement
- Zero sharp
- Von Neumann–Bernays–Gödel set theory
- Krull dimension of a noncommutative ring
- Morley rank
- Axiom of constructibility
- Gödel's consistency of CH and AC
- Jensen's covering theorem
- Cylindric algebra
- Borel hierarchy
- Supercompact cardinal
- Inner model
- Goodstein's theorem
- Class
- Surreal number
Further reading
- Web https://en.wikipedia.org/wiki/Ordinal_number, lead section
About this page
| Tag | 0YSCSX5YZC |
|---|---|
| URI | m2://0YSCSX5YZC |
| Aliases | ordinal, von-neumann-ordinal |
| Kind | concept |
| Writing | W1 stated |
| MSC | 03E10 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Used by
- Long line
- Von Neumann universe
- Constructible universe
- Proof-theoretic ordinal
- Burali-Forti paradox
- Tychonoff plank
- Ulm's theorem
- Axiom schema of replacement
- Zero sharp
- Krull dimension of a noncommutative ring
- Morley rank
- Axiom of constructibility
- Jensen's covering theorem
- Cylindric algebra
- Borel hierarchy
- Supercompact cardinal
- Inner model
- Goodstein's theorem
- Class
- Surreal number