洛阳师范学院学报
洛暘師範學院學報
락양사범학원학보
JOURNAL OF LUOYANG TEACHERS' COLLEGE
2014年
2期
4-5
,共2页
模型论%紧致性定理%无扭Abel群
模型論%緊緻性定理%無扭Abel群
모형론%긴치성정리%무뉴Abel군
model theory%compactness theorem%a torsion free group Abel model
文章用模型论中的紧致性定理证明了若L中理论T有任意可数阶的Abel群模型，则T有无扭Abel群模型；若一个语句φ在任意一个无扭Abel群中真，则对任意大的自然数n，存在自然数m＞n，使φ在m阶Abel群中真。最后证明了无扭Abel群不能有限公理化。
文章用模型論中的緊緻性定理證明瞭若L中理論T有任意可數階的Abel群模型，則T有無扭Abel群模型；若一箇語句φ在任意一箇無扭Abel群中真，則對任意大的自然數n，存在自然數m＞n，使φ在m階Abel群中真。最後證明瞭無扭Abel群不能有限公理化。
문장용모형론중적긴치성정리증명료약L중이론T유임의가수계적Abel군모형，칙T유무뉴Abel군모형；약일개어구φ재임의일개무뉴Abel군중진，칙대임의대적자연수n，존재자연수m＞n，사φ재m계Abel군중진。최후증명료무뉴Abel군불능유한공이화。
The author proved by the compactness theorem that if the theory of T with arbitrary countable order Abel group model in a formal language L then T has a torsion free group Abel model .If aφstatement is true in an arbitrary torsion free group Abel , then for a natural number n with arbitrarily large , there is a natural number m , which is larger than the natural number n , such that theφstatement is true in a group Abel with order m .At last , the author proved that a torsion free group Abel is not finitely axiomatizable in a formal language L .
