转移公理是什么意思？

    在上世纪70年代，美国数学家鲁宾逊创立非标准微积分，引入无穷小以及超实数系统，依靠的就是这条转移公理（Tranfer Axiom），但是，当时人们不熟悉数理逻辑模型论，思想上接受不了这条“怪怪”的公理。

老实说，我们的00后大学生都熟悉处理PDF文件，手指双击“Elementary Calculus”图标，找到转移公理的陈述并不费事。

如今，时代前进了，死死抱着菲氏微积分这个“老古董”，不好意思。菲氏老翁死前，模型论还没有诞生呢！

请见附件中对转移公理的说明。

    今天是我80岁生日，很快乐！

袁萌  7月17日

附：

TRANSFER AXIOM

Every real statement that holds for all real numbers holds for all hyperreal

numbers.

It is possible to develop the whole calculus course as presented in this

book from these axioms for the real and hyperreal numbers. By the Transfer Axiom,

all the Algebraic Axioms for the Real Numbers also hold true for the hyperreal

numbers. In other words, we can transfer every Algebraic Axiom for the real numbers to the hyperreal numbers. We can also transfer every Order Axiom for the real numbers to the hyperreal numbers. The Trichotomy Law is part of the Extension Axiom. Each of the other Order Axioms is a real statement and thus carries over to the hyperreal numbers by the Transfer Axiom. Thus we can make computations with the hyperreal numbers in the same way as we do for the real numbers.（全文完）