| dbo:abstract |
Alternativní teorie množin obecně je alternativní matematický přístup ke konceptu množiny. Je to navrhovaná alternativa k standardní teorii množin. Některé z alternativních teorií množin: * teorie polomnožin * teorie * teorie neostrých množin * teorie množin New Foundations * teorie Alternativní teorie množin (nebo ATM) je také specifický název konkrétní teorie vyvinuté v 70. - 80. letech 20. století Petrem Vopěnkou a jeho studenty. Staví na některých myšlenkách teorie polomnožin, ale zavádí i radikálnější změny: např.: všechny množiny jsou konečné (ačkoliv některé jsou "nestandardně konečné" a externě ve skutečnosti nekonečné, a v ATM existují také třídy, které mohou být nekonečné i interně. (cs) In a general sense, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory. More specifically, Alternative Set Theory (or AST) may refer to a particular set theory developed in the 1970s and 1980s by Petr Vopěnka and his students. (en) 一般來講，可替代的集合论（an alternative set theory）是指建立集合概念的其它数学方法。它的正是作為標準集合論的替代而出現的。 一些可替代的集合论： * 半集合理论 * 粗集合理论 * 模糊集理论 * 新基础集合论 (NF) * 正集合论 狹義地，可替代集合論（the Alternative Set Theory，AST）是指一種具體的集合論，它是在70年代至80年代之間由和他的学生所發展的。此理論建立於半集合理论的某些想法上，但也引入了更加激进的改变：例如，在 AST 中所有集合都是「形式上」有限的，也就是說關於集合公式的數學歸納法成立（更精確地說，AST 中只和集合有關的那些公理，和ZF集合論是等價的。其中，無窮公理被它的否命題取代了）。但是這些形式上有限的集合中，有一些包含了不是集合的子類，這使之與康托所定義的有限集（ZF的有限集）有所不同。這些子類稱作AST中的無窮集（尽管一些是"非标准有限的"而外在的实际上无限的，还有甚至类可以内在的是无限的）。 (zh) |
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In a general sense, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory. More specifically, Alternative Set Theory (or AST) may refer to a particular set theory developed in the 1970s and 1980s by Petr Vopěnka and his students. (en) 一般來講，可替代的集合论（an alternative set theory）是指建立集合概念的其它数学方法。它的正是作為標準集合論的替代而出現的。 一些可替代的集合论： * 半集合理论 * 粗集合理论 * 模糊集理论 * 新基础集合论 (NF) * 正集合论 狹義地，可替代集合論（the Alternative Set Theory，AST）是指一種具體的集合論，它是在70年代至80年代之間由和他的学生所發展的。此理論建立於半集合理论的某些想法上，但也引入了更加激进的改变：例如，在 AST 中所有集合都是「形式上」有限的，也就是說關於集合公式的數學歸納法成立（更精確地說，AST 中只和集合有關的那些公理，和ZF集合論是等價的。其中，無窮公理被它的否命題取代了）。但是這些形式上有限的集合中，有一些包含了不是集合的子類，這使之與康托所定義的有限集（ZF的有限集）有所不同。這些子類稱作AST中的無窮集（尽管一些是"非标准有限的"而外在的实际上无限的，还有甚至类可以内在的是无限的）。 (zh) Alternativní teorie množin obecně je alternativní matematický přístup ke konceptu množiny. Je to navrhovaná alternativa k standardní teorii množin. Některé z alternativních teorií množin: * teorie polomnožin * teorie * teorie neostrých množin * teorie množin New Foundations * teorie (cs) |
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