Admissible ordinal

In set theory, an ordinal number α is an admissible ordinal if L_α is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other words, α is admissible when α is a limit ordinal and L_α⊧Σ₀-collection.

The first two admissible ordinals are ω and $\omega_1^{\mathrm{CK}}$ (the least non-recursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal.

单词	Admissible ordinal
释义	Admissible ordinal 英语百科 Admissible ordinal In set theory, an ordinal number α is an admissible ordinal if L_α is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other words, α is admissible when α is a limit ordinal and L_α⊧Σ₀-collection. The first two admissible ordinals are ω and $\omega_1^{\mathrm{CK}}$ (the least non-recursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal.
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