超穷序集及超穷论法

Tranfinite Ordered Set and Transfinite Induction

给出了序集W为半整序集的充要条件是W的非空真前段有形A（x0）及A［x0］。在半整序集上建立了超穷归纳法原理：设W是一个半整序集，P是一个性质，如果下列命题成立，则W的所有元素均具有性质P．（1）若α＜x＜β具有性质P，则α，β具有性质P；（2）一串不具有性质P的点的极限点亦不具有性质P．

Some theorems on semi-well-ordered set are given as follows- An ordered set is semi-wellordered set if and only if its every no-null initial has the form A(x0) or A[x0].If W is a eemi-well-ordered set, P is a proposition, then.the proposition P holds for all x∈W, if(1) Its truth for all elements a<x<β implies its truth for α,β;(2) An ordered-point set without P implies that its limiting point does not hold P.