集合族

Multi tool use
在集合论和有关的数学分支中,给定集合S的子集的搜集F叫做S的子集族或S上的集合族。更一般的说,无论什么任何集合的搜集都叫做集合族。
例子
幂集P(S)是在S上的集合族。
- n元素集合S的k元素子集S(k)形成了集合族。
- 所有序数的类Ord是“大”集合族;它自身不是集合而是真类。
- 样本空间的某些子集组成的集合叫做集合族。
性质
S的任何子集族自身都是幂集P(S)的子集。
- 不论什么集合族都是所有集合的真类(全集)V的子类。
超图是集合V(顶点集合)加上V的非空子集族(边)。
参见
集合论
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公理 |
选择
- 外延
- 无穷
- 配对
- 幂集
- 正则性
- 并集
- 马丁公理
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运算 |
- 笛卡儿积
- 德摩根定律
- 交集
- 冪集
- 补集
- 对称差
- 并集
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- 势
基数(大基数)
- 类
- 可构造全集
- 连续统假设
- 對角論證法
元素
- 集合族
- 力迫
- 一一对应
- 序数
- 超限归纳法
- 文氏图
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集合类型 |
- 可數集
- 空集
有限集合(继承有限集合)
- 模糊集
- 无限集合
- 递归集合
- 子集
- 传递集合
- 不可數集
- 泛集
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理论 |
策梅洛
数学原理
策梅洛-弗兰克
冯诺伊曼-博内斯-哥德尔
- 克里普克–普拉特克
- 塔斯基–格罗滕迪克
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- 罗素悖论
- 萨斯林问题
- ZFC系統無法確定的命題列表
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集合論者 |
- 亚伯拉罕·弗兰克尔
- 伯特兰·罗素
- 恩斯特·策梅洛
- 格奥尔格·康托尔
- 约翰·冯·诺伊曼
- 库尔特·哥德尔
- 盧菲特·澤德
- 保尔·贝尔奈斯
- 保罗·寇恩
- 理查德·戴德金
- 托马斯·耶赫
- 威拉德·蒯因
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