inaccessible aleph - vertaling naar russisch
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inaccessible aleph - vertaling naar russisch

CARDINAL UNOBTAINIBLE FROM SMALLER CARDINALS VIA USUAL CARDINAL ARITHMETIC
Strongly inaccessible cardinal; Weakly inaccessible cardinal; Inaccessible cardinals axiom; Hyper-inaccessible cardinal; Inaccessible cardinals; Accessible cardinal; Weakly inaccessible; Strongly inaccessible

inaccessible aleph      

математика

недостижимый алеф

inaccessible cardinal         

математика

недостижимое кардинальное число

weakly inaccessible         

математика

слабо недостижимый

Definitie

Aleph
<text, language> ["Aleph: A language for typesetting", Luigi Semenzato <luigi@cs.berkeley.edu> and Edward Wang <edward@cs.berkeley.edu> in Proceedings of Electronic Publishing, 1992 Ed. Vanoirbeek & Coray Cambridge University Press 1992]. (1994-12-15)

Wikipedia

Inaccessible cardinal

In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic. More precisely, a cardinal κ is strongly inaccessible if it is uncountable, it is not a sum of fewer than κ cardinals smaller than κ, and α < κ {\displaystyle \alpha <\kappa } implies 2 α < κ {\displaystyle 2^{\alpha }<\kappa } .

The term "inaccessible cardinal" is ambiguous. Until about 1950, it meant "weakly inaccessible cardinal", but since then it usually means "strongly inaccessible cardinal". An uncountable cardinal is weakly inaccessible if it is a regular weak limit cardinal. It is strongly inaccessible, or just inaccessible, if it is a regular strong limit cardinal (this is equivalent to the definition given above). Some authors do not require weakly and strongly inaccessible cardinals to be uncountable (in which case 0 {\displaystyle \aleph _{0}} is strongly inaccessible). Weakly inaccessible cardinals were introduced by Hausdorff (1908), and strongly inaccessible ones by Sierpiński & Tarski (1930) and Zermelo (1930).

Every strongly inaccessible cardinal is also weakly inaccessible, as every strong limit cardinal is also a weak limit cardinal. If the generalized continuum hypothesis holds, then a cardinal is strongly inaccessible if and only if it is weakly inaccessible.

0 {\displaystyle \aleph _{0}} (aleph-null) is a regular strong limit cardinal. Assuming the axiom of choice, every other infinite cardinal number is regular or a (weak) limit. However, only a rather large cardinal number can be both and thus weakly inaccessible.

An ordinal is a weakly inaccessible cardinal if and only if it is a regular ordinal and it is a limit of regular ordinals. (Zero, one, and ω are regular ordinals, but not limits of regular ordinals.) A cardinal which is weakly inaccessible and also a strong limit cardinal is strongly inaccessible.

The assumption of the existence of a strongly inaccessible cardinal is sometimes applied in the form of the assumption that one can work inside a Grothendieck universe, the two ideas being intimately connected.

Vertaling van &#39inaccessible aleph&#39 naar Russisch