无穷小微积分植根于现代模型论沃土之中
当前，国内有人认为，无穷小微积分是邪门怪盗，不是正统数学。这是不正确的。
在国外，无穷小微积分（即鲁宾逊无穷小分析）被认定为，是模型论的一个数学重要分支，鲁宾逊与塔尔斯基、哥德尔齐名，堂堂正正，不是邪门怪盗。
今年9月，大批00后青年学子即将进入大学学习微积分基础课。选择基于极限轮的菲氏微积分，还是选择基于现代模型论的无穷小微积分是一个不可回避的现实问题，不能误人子弟。
关于现代模型论的数学分株，请见本文附件。
袁萌 7月7日
附：Branches of model theory
This articlefocuses on finitary first order model theory of infinite structures. Finitemodel theory, which concentrates on finite structures, diverges significantlyfrom the study of infinite structures in both the problems studied and thetechniques used. Model theory in higher-order logics or infinitary logics ishampered by the fact that completeness and compactness do not in general holdfor these logics. However, a great deal of study has also been done in suchlogics.
Informally, model theory can be divided intoclassical model theory, model theory applied to groups and fields, andgeometric model theory. A missing subdivision is computable model theory, butthis can arguably be viewed as an independent subfield of logic.
（请读者注意这段话）Examples of earlytheorems from classical model theory include （哥德尔）Gödel'scompleteness theorem, the upward and downward Löwenheim–Skolem theorems,Vaught's two-cardinal theorem, Scott's isomorphism theorem, the omitting typestheorem, and the Ryll-Nardzewski theorem. Examples of early results from modeltheory applied to fields are （塔尔斯基）Tarski's elimination ofquantifiers for real closed fields, Ax's theorem on pseudo-finite fields, and （鲁宾逊）Robinson'sdevelopment of non-standard analysis. （注意对其评论）An important stepin the evolution of classical model theory occurred with the birth of stabilitytheory (through Morley's theorem on uncountably categorical theories andShelah's classification program), which developed a calculus of independenceand rank based on syntactical conditions satisfied by theories.
During the lastseveral decades applied model theory has repeatedly merged with the more purestability theory. The result of this synthesis is called geometric model theoryin this article (which is taken to include o-minimality, for example, as wellas classical geometric stability theory). An example of a theorem fromgeometric model theory is Hrushovski's proof of the Mordell–Lang conjecture forfunction fields. The ambition of geometric model theory is to provide ageography of mathematics by embarking on a detailed study of definable sets invarious mathematical structures, aided by the substantial tools developed inthe study of pure model theory.（全文完）