非标准分析方法
An approach to non-standard analysis
摘要：
本说明有两个主要目的：将非标准分析的本质描述为一种特殊的结构（我们称之为lim-rim），注意到它与超能力概念的相互作用，并提出了一个非标准分析的结构，被视为数学问题，其中集合A -“所有可能极限的附加”的非标准元的集合 *A是“好”类的极限，边缘，其作用类似于域的代数闭包-“多项式的所有根的附加”。在与代数闭包相同的精神下，只要有足够的广义连续统假设，就有直到同构的唯一性，也有普适性和齐性。*A的基数大约是2^（2^ |A|），并且具有高饱和度。
英文摘要：
This note has two principal aims: to portray an essence of Non-Standard Analysis as a particular structure (which we call lim-rim), noting its interplay with the notion of ultrapower, and to present a construction of Non-Standard Analysis, viewed as a matter of mathematics, where the set *A of non-standard elements of a set A - "the adjunction of all possible limits" is a "good" kind of lim-rim which plays a role analogous to the algebraic closure of a field - "the adjunction of all roots of polynomials". In the same spirit as with algebraic closures, one has uniqueness up to isomorphism, and also universality and homogeneity, provided one has enough Generalized Continuum Hypothesis. The cardinality of *A will be just something like 2^(2^|A|), and one has a high degree of saturation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
