Concept

Remarkable cardinal

Résumé
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 = HρN, i.e., M ∈ N and N ⊨ "M is the set of all sets that are hereditarily smaller than ρ" Equivalently, is remarkable if and only if for every there is such that in some forcing extension , there is an elementary embedding satisfying . Although the definition is similar to one of the definitions of supercompact cardinals, the elementary embedding here only has to exist in , not in .
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.