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| remarkable cardinal ： ウィキペディア英語版 |
remarkable cardinal
In mathematics, a remarkable cardinal is a certain kind of large cardinal number.
A cardinal κ is called remarkable if for all regular cardinals θ > κ, there exist π, ''M'', λ, σ, ''N'' and ρ such that
# π : ''M'' → Hθ is an elementary embedding
# ''M'' is countable and transitive
# π(λ) = κ
# σ : ''M'' → ''N'' is an elementary embedding with critical point λ
# ''N'' is countable and transitive
# ρ = ''M'' ∩ Ord is a regular cardinal in ''N''
# σ(λ) > ρ
# ''M'' = ''H''ρ''N'', i.e., ''M'' ∈ ''N'' and ''N'' ⊨ "''M is the set of all sets that are hereditarily smaller than ρ''"
==See also==
*Hereditarily countable set
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「remarkable cardinal」の詳細全文を読む
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