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单词 Saturated model
释义

Saturated model

中文百科

饱和模型

在模型论中,饱和模型可以大致描述为一个实现够小的型的模型。

κ 为一个基数,\mathcal{M} 为某个一阶语言中对某理论的模型。\mathcal{M} 被称作是 κ-饱和 的,当且仅当对所有基数小于 κ 的子集 A \subset \mathcal{M},以 A 为参数的完备型都被 \mathcal{M} 实现。\mathcal{M} 被称作是饱和的,当且仅当它是 |\mathcal{M}|-饱和的。

英语百科

Saturated model 饱和模型

In mathematical logic, and particularly in its subfield model theory, a saturated model M is one which realizes as many complete types as may be "reasonably expected" given its size. For example, an ultrapower model of the hyperreals is \aleph_1-saturated, meaning that every descending nested sequence of internal sets has a nonempty intersection, see Goldblatt (1998).

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