# ⓘ Ineffable cardinal. In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by Jensen & Kunen. A ..

## ⓘ 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