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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Countable ordinal

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Summary

An ordinal whose underlying set is finite or countably infinite.

Record metadata

Canonical name: Countable ordinal
Concept ID: countable_ordinal
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Set theory
Domains: Set theory, Order theory, Logic
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Ordinal class

Carrier(s)

ordinal $\alpha$

Axioms / constraints

there is an injection $\alpha\to\omega$

Notes

The collection of all countable ordinals is itself uncountable and forms $\omega_1$ .

Concept sources

Wikipedia — First uncountable ordinal — First uncountable ordinal · encyclopedic reference · source ID wp-first-uncountable-ordinal
nLab — Countable ordinal — Countable ordinal · mathematical reference · source ID nlab-countable-ordinal
Open Logic Project — Set Theory — Open Logic Project: Set Theory · open textbook source · source ID openlogic-set-theory

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Ordinal Countable ordinal

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: ordinal_to_countable_ordinal
Relation type: Classification classification
Direction: source → target
Endpoint roles: source: Has subtype; target: Classified as
Authored annotation: countable ordinals

Authored explanation

Countable ordinals are the ordinals admitting an injection into $\omega$ .

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources

Wikipedia — First uncountable ordinal — First uncountable ordinal · encyclopedic reference · source ID wp-first-uncountable-ordinal

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.