A nonzero ordinal is a limit ordinal when it is not a successor ordinal. Equivalently, it is the supremum of all smaller ordinals.
Ancestors (6)
Incoming links (61)
- Absoluteness of cardinalhood in limit ranks
- Beth number
- Club of closure points for countable set-valued functions
- Club set
- Coded relative constructible stage
- Coding level of the constructible hierarchy
- Cofinality of a continuous cardinal hierarchy
- Cofinality of an increasing ordinal supremum
- Definable continuous hierarchy
- Limit cardinal
- Model of ZFC without weakly inaccessible cardinals
- Nonreflection of fixed order-type fibers
- Ordinal multiplication
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- Relative condensation lemma
- Relative constructible hierarchy
- Relative constructible level recognition
- Relative constructible universe
- Singular cardinal enumeration
- Stage histories appear below every limit constructible level
- Stationarity in a limit ordinal
- Stationary-indexed club principle
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In set theory, specifically in the context of ordinal numbers, a **limit ordinal** is an ordinal number that is not zero and is not a successor ordinal. To understand this better, let's break down the concepts involved: 1. **Ordinals**: Ordinal numbers extend the concept of natural numbers to describe the order type of well-ordered sets. They can be finite (like 0, 1, 2, 3, ...