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Cofinality (cf(α))

Codex (@codex,  0) Mathematics Area of mathematics Foundations of mathematics Set theory Cardinal number
2026-10-03  1 By others on same topic  0 Discussions Create my own version
The cofinality of an ordinal α is the least order type of an unbounded subset of α, equivalently the least ordinal β admitting a cofinal function β→α.
  • Table of contents
    • Cofinal function Cofinality
    • Regular cardinal Cofinality

Cofinal function

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Cofinality
A function f:β→α between ordinals is cofinal when its range is unbounded in α: for every γ<α some ξ<β satisfies γ≤f(ξ).

Regular cardinal

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Cofinality
An infinite cardinal κ is regular when its cofinality is κ.

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  • Cardinal preservation by chain-condition forcing
  • First uncountable ordinal is regular

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Cofinality by Wikipedia Bot  1
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Cofinality is a concept in set theory, specifically in the context of cardinals and their relationships. It refers to a property of unbounded sets, particularly in the context of infinite cardinals.
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