ⓘ Ineffable cardinal
In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by Jensen & Kunen.
A cardinal number κ {\displaystyle \kappa } is called almost ineffable if for every f: κ → P κ {\displaystyle f:\kappa \to {\mathcal {P}}\kappa} where P κ {\displaystyle {\mathcal {P}}\kappa} is the powerset of κ {\displaystyle \kappa }) with the property that f δ {\displaystyle f\delta} is a subset of δ {\displaystyle \delta } for all ordinals δ < κ {\displaystyle \delta
 almost ineffable ineffable n  ineffable totally ineffable cardinals remarkable cardinals α  Erdos cardinals for countable α 0 not a cardinal γ  iterable
 the subsets of cardinality n from A. A cardinal κ is called ineffably Ramsey if A can be chosen to be stationary subset of κ. A cardinal κ is called virtually
 infinite ordinal α κ form a set of cardinality at most α. The Kurepa hypothesis is false if κ is an ineffable cardinal and conversely Jensen showed that
 Ramsey cardinal Erdos cardinal Extendible cardinal Huge cardinal Hyper  Woodin cardinal Inaccessible cardinal Ineffable cardinal Mahlo cardinal Measurable
 measurable cardinal is inaccessible and is ineffable Ramsey, etc. it is consistent with ZF that a measurable cardinal can be a successor cardinal It follows
 Mathematical Logic, 9: 187 222, 1976 Baumgartner, James E., Ineffability properties of cardinals I, Infinite and Finite Sets, Keszthely Hungary 1973, volume
 all large cardinal axioms that are realized in L such as being totally ineffable It follows that the existence of 0 contradicts the axiom of constructibility:
 The foundation Pro Oriente was founded in 1964 by the Viennese cardinal Franz Konig to improve relationships between the Roman Catholic and the Eastern
 non  empty ordered subset has an upper bound ineffable cardinal An ineffable cardinal is a type of large cardinal related to the generalized Kurepa hypothesis
 incarnate Word, perfectus Deus, perfectus homo cf. Creed Quicumque In his ineffable love, the crucified Christ reveals in a striking way the Father s infinite
 Cologne then said the prayers, Bless, Lord, this king, ...etc. and Ineffable God, ...etc. The Archbishop then anointed him with the oil of the catechumens

Large cardinal 
Axiom of determinacy 

Berkeley cardinal 
Core model 
Critical point (set theory) 
Extender (set theory) 

Extendible cardinal 
Grothendieck universe 
Huge cardinal 
Indescribable cardinal 
Iterable cardinal 
Kunens inconsistency theorem 
Mahlo cardinal 
Measurable cardinal 

Rankintorank 
Reinhardt cardinal 
Remarkable cardinal 
Shelah cardinal 
Shrewd cardinal 
Strong cardinal 
Strongly compact cardinal 
Quasicompact cardinal 
Unfoldable cardinal 
Weakly compact cardinal 
Wholeness axiom 
Woodin cardinal 
Zero sharp 

Film 

Television show 

Game 

Sport 

Science 

Hobby 

Travel 

Technology 

Brand 

Outer space 

Cinematography 

Photography 

Music 

Literature 

Theatre 

History 

Transport 

Visual arts 

Recreation 

Politics 

Religion 

Nature 

Fashion 

Subculture 

Animation 

Award 

Interest 