论非标准时空连续统模型及其对Zeno悖论分析的应用

1960年美国数理逻辑学家A.Robinson运用现代数理逻辑方法成功地构造出包含无限小和无限大等非标准数在内的数域~*R,并在~*R上建立了非标准分析理论。1980年,本文作者之一及其合作者曾引进了一个非康托自然数序列模型,其中包含着,v为无限自然数},(ω) 为ω的银河(Galaxy)。N及被解释为生成观点下的无限性总体。这一模型的特点是包含这个有限与无限之间即与(ω)之间的潜变段或飞跃段。中的元素v是既非有限又非无限的潜变无限大。飞跃段的

On the Non-standard Model for the Time and Space with an Application to Resolving Zeno s Paradoxes

The object of this article is to expound our non-standard model <^*R, N> for the time and space, in which ^*R is the non-standard real continuum and N the flying segment of N-the so-called non -Cantorian model of natural number sequence whose structure has been formulated previously (cf. Lizhi Xu's book "Selected Topics on the Methodology of Mathematics", Hua Zhong University of Science & Technology Press, 1983, Cha pter 7). As an application of the model, Zeno's paradoxes have been resolved in a very natural way. In fact, the concept of motion and that of motionlessness have only relative meaning with respect to the so-called monads of different orders in the model <^*R, N>.