e/Large cardinal

Information
has gloss	eng: In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than aleph zero, bigger than the cardinality of the continuum, etc.). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".
lexicalization	eng: Large cardinal hypotheses
lexicalization	eng: Large cardinals
lexicalization	eng: large cardinal
subclass of	(noun) (Roman Catholic Church) one of a group of more than 100 prominent bishops in the Sacred College who advise the Pope and elect new Popes cardinal
has instance	e/cs/Kunenova bariéra
has instance	e/cs/Slabě kompaktní kardinál
has instance	e/cs/Slabě nedosažitelný kardinál
has instance	e/Core model
has instance	e/Critical point (set theory)
has instance	e/Equiconsistency
has instance	e/Erdoes cardinal
has instance	e/Extender (set theory)
has instance	e/Extendible cardinal
has instance	e/Grothendieck universe
has instance	e/Homogeneous (large cardinal property)
has instance	e/Huge cardinal
has instance	e/Indescribable cardinal
has instance	e/Ineffable cardinal
has instance	e/Jónsson cardinal
has instance	e/Kunen's inconsistency theorem
has instance	e/Laver function
has instance	e/List of large cardinal properties
has instance	e/Mahlo cardinal
has instance	e/Ramsey cardinal
has instance	e/Rank-into-rank
has instance	e/Reflecting cardinal
has instance	e/Reinhardt cardinal
has instance	e/Remarkable cardinal
has instance	e/Rowbottom cardinal
has instance	e/Shelah cardinal
has instance	e/Shrewd cardinal
has instance	e/Solovay model
has instance	e/Strong cardinal
has instance	e/Strongly compact cardinal
has instance	e/Subcompact cardinal
has instance	e/Subtle cardinal
has instance	e/Supercompact cardinal
has instance	e/Superstrong cardinal
has instance	e/Unfoldable cardinal
has instance	e/Weakly compact cardinal
has instance	e/Woodin cardinal
has instance	e/Zero dagger

Meaning
Czech
has gloss	ces: Velké kardinály či velká kardinální čísla je v teorii množin souhrnné označení pro kardinální čísla, jejichž existence je nezávislá na axiomech Zermelo-Fraenkelovy teorie s axiomem výběru (ZFC). Existence či neexistence každého z těchto čísel má v ZF závažné důsledky týkající se zejména nekonečné kombinatoriky. Často však přijetí axiomu postulujícího existenci nějakého velkého kardinálu zásadně ovlivňuje vlastnosti o kardinálech malých (\alef_1, \alef_2, …).
lexicalization	ces: velké kardinály
German
has gloss	deu: * \kappa heißt schwach unerreichbare Kardinalzahl, wenn sie überabzählbarer, regulärer Limes ist, wenn also \mathrmcf} (\kappa) = \kappa > \omega (cf steht für Konfinalität) gilt und für jedes \mu < \kappa auch \mu^+ < \kappa. Schwach unerreichbare Kardinalzahlen sind genau die regulären Fixpunkte der Aleph-Reihe: \aleph_\kappa = \kappa = \mathrmcf} (\kappa). * \kappa heißt stark unerreichbare Kardinalzahl, wenn \kappa überabzählbarer, regulärer starker Limes ist, wenn also \mathrmcf} (\kappa) = \kappa > \omega gilt und für jedes \mu < \kappa auch 2^\mu < \kappa. Stark unerreichbare Kardinalzahlen sind genau die regulären Fixpunkte der Beth-Reihe: \beth_\kappa = \kappa = \mathrmcf} (\kappa).
lexicalization	deu: Große Kardinalzahl
Esperanto
lexicalization	epo: Grandaj kardinaloj
French
has gloss	fra: En mathématiques, et plus précisément en théorie des ensembles, un grand cardinal est un nombre cardinal transfini satisfaisant une propriété qui le distingue des ensembles constructibles avec laxiomatique usuelle (ZFC) tels que aleph zéro, aleph-ω, etc., et le rend nécessairement plus grand que tous ceux-ci. Lexistence dun grand cardinal est donc soumise à lacceptation de nouveaux axiomes.
lexicalization	fra: grand cardinal
Korean
lexicalization	kor: 큰 기수
Polish
has gloss	pol: Duże liczby kardynalne (ang. large cardinals) – liczby kardynalne których istnienia nie można udowodnić w ZFC i co więcej takie, dla których niesprzeczność istnienia nie wynika z niesprzeczności ZFC, a jednocześnie można wykazać niesprzeczność nieistnienia tych liczb.
lexicalization	pol: Duże liczby kardynalne
Portuguese
has gloss	por: No campo matemático da teoria dos conjuntos, uma propriedade de grande cardinal é um certo tipo de propriedade de números cardinais transfinitos. Cardinais com tais propriedades, como o nome sugere, são muito "grandes" (por exemplo, maior que aleph (a cardinalidade dos números naturais), maiores que a cardinalidade do contínuo, et cetera).
lexicalization	por: Propriedade de grande cardinal

Word:	(case sensitive)
Language:	(ISO 639-3 code, e.g. "eng" for English)

e/Large cardinal

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