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Imbedding a Finite Metric set in an N-Dimensional Minkowski Space 1)1)This paper is a revision of part of the author’s doctoral dissertation at the University of Pennsylvania, prepared under the direction of Professor I. J. Schoenberg.

机译：在N维Minkowski空间中嵌入有限度量集1）1）本文是宾夕法尼亚大学在I. J. Schoenberg教授的指导下编写的部分博士论文的修订版。

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Wolfe Dorothy;
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年度 1967
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1. Certain Simple, Unsolvable Problems of Group Theory. V 29,3029Parts I, II, III and IV have appeared in Series A, 57, Nos. 3 and 5; 58, Nos. 2 and 5 of these Proceedings, as well as Indag. Math., 16, Nos. 3 and 5 (1954); 17, Nos. 2 and 5 (1955).In Part I, page 234, the ninth and tenth lines following the displayed material, for both occurrences of A read D and for both occurrences of B read E: In part II, page 497, for all occurrences of M in Diagrams A and D read C. In Part IV, page 574, the third displayed line, for zαiLread z―αiL. 19).30The proof of the unsolvability of the word problem contained in this and subsequent paper is not contained in the dissertation Several simple unsolvable problems of group theory related to the word problem. (See footnote 1 of Part I.) Our proof was finally completed during the period 1954-56 while in residence at the Institute for Advanced Study. We were supported in 1954-55 directly by the Institute and in 1955-56 by National Science Foundation contract G-1974. Certain improvements were evolved ans preparations for publication were completed while the author held a Fulbright grant to the University of Oslo.Our thanks are due to Professor Kurt Gödel for his kind encouragement in these matter; certain related problems for study he has suggested we hope to deal with later. When an earlier version of Lemmas 30 and 31 was explained at a colloquium at the University of Michigan, August 3, 1956, Professor Roger Lyndon suggested an improvement which is incorporated in our present version. We are indeed indebted to Dr. John Addison and Dr. Michael Rabin for checking many of the new details during July of 1956.) [O] . Boone William W. 1957

机译：群体理论的某些简单，不可解决的问题。 V 29,3029 I，II，III和IV部分出现在A系列57、3和5号中； 58，第2和5号程序，以及Indag。 Math。，16，Nos 3 and 5（1954）; 》，第17卷，第2期和第5期（1955年）。在第一部分，第234页中，显示的材料之后的第九行和第十行，出现A读D和出现B都读E：在第二部分，第497页，对于图A和D中所有出现的M，请读C。在第Ⅳ部分，第574页中，第三行显示为zαiLreadz-αiL。 19）.30本论文及后续论文中所包含的单词问题的不可解性的证明不包含在本文中。（请参阅第I部分的脚注1。）我们的证明终于在1954-56年期间居住在高级研究所期间完成了。该研究所在1954-55年间直接为我们提供了支持，在1955-56年间得到了美国国家科学基金会的G-1974合同的支持。在作者获得奥斯陆大学富布赖特奖学金的同时，对出版物的改进和准备工作也有所进展。感谢库尔特·哥德尔教授在此方面的大力鼓励。他建议我们研究一些相关的问题，希望以后再解决。 1956年8月3日，在密歇根大学的一个座谈会上解释了Lemmas 30和31的早期版本时，Roger Lyndon教授建议进行改进，并将其纳入当前版本。我们确实要感谢John Addison博士和Michael Rabin博士在1956年7月检查了许多新细节。）

Imbedding a Finite Metric set in an N-Dimensional Minkowski Space 1)1)This paper is a revision of part of the author’s doctoral dissertation at the University of Pennsylvania, prepared under the direction of Professor I. J. Schoenberg.

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