| dbo:abstract |
Měřitelný kardinál je matematický pojem z oblasti teorie množin (kardinální aritmetiky). Patří mezi velké kardinály. (cs) In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α}, α ∈ κ are small, complements of small sets are large and vice versa. The intersection of fewer than κ large sets is again large. It turns out that uncountable cardinals endowed with a two-valued measure are large cardinals whose existence cannot be proved from ZFC. The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930. (en) En mathématiques, un cardinal mesurable est un cardinal sur lequel existe une mesure définie pour tout sous-ensemble. Cette propriété fait qu'un tel cardinal est un grand cardinal. (fr) 집합론에서 가측 기수(可測基數, 영어: measurable cardinal)는 기본 매장으로 정의될 수 있는 기수이다. 큰 기수의 하나이다. (ko) Liczba mierzalna – nieprzeliczalna liczba kardynalna na której istnieje -zupełny niegłówny ultrafiltr. Liczba rzeczywiście mierzalna to nieprzeliczalna liczba kardynalna na której istnieje -addytywna miara, która znika na punktach i która mierzy wszystkie podzbiory Liczby mierzalne są punktem wyjściowym dla części hierarchii dużych liczb kardynalnych związanej z zanurzeniami elementarnymi V w model wewnętrzny M. (pl) Em matemática, especialmente em teoria dos conjuntos, um cardinal não enumerável é denominado mensurável se existe uma medida -aditiva, valorada em (ou seja, bivalente) e náo trivial sobre o conjunto potência . Cardinal mensurável é considerada uma propriedade de grande cardinal. (pt) 數學上，可測基數是一類大基數。為了定義此概念，考慮基數 κ 上僅取兩值（0 或 1）的測度。如此的測度可看成將 κ 的所有子集分成兩類：大和小，使得 κ 本身為大，但 ∅ 和所有單元素集合 皆為小，且小集的補集為大，反之亦然。同時還要求少於 κ 個大集的交集仍為大。 具有以上二值測度的不可數基數是大基數，ZFC 無法證明其存在。 可測基數的概念最早由斯塔尼斯拉夫·烏拉姆於 1930 年提出。 (zh) |
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https://eudml.org/doc/212126 https://eudml.org/doc/212335 https://eudml.org/doc/212487 https://semanticscholar.org/paper/8d3d986c97fa971246dffd101c411d4e071c4155 http://faculty.sites.uci.edu/pjmaddy/bibliography/ |
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Stanislaw Ulam (en) Stefan Banach (en) |
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Stefan (en) Stanislaw (en) |
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Banach (en) Ulam (en) |
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Měřitelný kardinál je matematický pojem z oblasti teorie množin (kardinální aritmetiky). Patří mezi velké kardinály. (cs) En mathématiques, un cardinal mesurable est un cardinal sur lequel existe une mesure définie pour tout sous-ensemble. Cette propriété fait qu'un tel cardinal est un grand cardinal. (fr) 집합론에서 가측 기수(可測基數, 영어: measurable cardinal)는 기본 매장으로 정의될 수 있는 기수이다. 큰 기수의 하나이다. (ko) Liczba mierzalna – nieprzeliczalna liczba kardynalna na której istnieje -zupełny niegłówny ultrafiltr. Liczba rzeczywiście mierzalna to nieprzeliczalna liczba kardynalna na której istnieje -addytywna miara, która znika na punktach i która mierzy wszystkie podzbiory Liczby mierzalne są punktem wyjściowym dla części hierarchii dużych liczb kardynalnych związanej z zanurzeniami elementarnymi V w model wewnętrzny M. (pl) Em matemática, especialmente em teoria dos conjuntos, um cardinal não enumerável é denominado mensurável se existe uma medida -aditiva, valorada em (ou seja, bivalente) e náo trivial sobre o conjunto potência . Cardinal mensurável é considerada uma propriedade de grande cardinal. (pt) 數學上，可測基數是一類大基數。為了定義此概念，考慮基數 κ 上僅取兩值（0 或 1）的測度。如此的測度可看成將 κ 的所有子集分成兩類：大和小，使得 κ 本身為大，但 ∅ 和所有單元素集合 皆為小，且小集的補集為大，反之亦然。同時還要求少於 κ 個大集的交集仍為大。 具有以上二值測度的不可數基數是大基數，ZFC 無法證明其存在。 可測基數的概念最早由斯塔尼斯拉夫·烏拉姆於 1930 年提出。 (zh) In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α}, α ∈ κ are small, complements of small sets are large and vice versa. The intersection of fewer than κ large sets is again large. The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930. (en) |
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Měřitelný kardinál (cs) Cardinal mesurable (fr) 가측 기수 (ko) Measurable cardinal (en) Liczba mierzalna (pl) Cardinal mensurável (pt) 可測基數 (zh) |
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