The Exponential-Logarithmic Equivalence Classes of Surreal Numbers

被引：0
作者：
Salma Kuhlmann
Mickaël Matusinski
机构：
[1] Universität Konstanz,Fachbereich Mathematik und Statistik
[2] Université Bordeaux 1,Institut de Mathématiques de Bordeaux
来源：
Order | 2015年 / 32卷
关键词：
Surreal numbers; Real exponential logarithmic field; Primary 12J15; 03H05; Secondary 03E10; 06A05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In his monograph, H. Gonshor showed that Conway’s real closed field of surreal numbers carries an exponential and logarithmic map. In this paper, we give a complete description of the exponential equivalence classes in the spirit of the additive and multiplicative equivalence classes. This description is made in terms of a recursive formula as well as a sign sequence formula for the family of representatives of minimal length of these exponential classes.
引用
收藏
页码：53 / 68
页数：15
相关论文
共 20 条
  • [1] Ehrlich P(2001)Number systems with simplicity hierarchies: a generalization of Conway’s theory of surreal numbers J. Symbolic Logic 66 1231-1258
  • [2] Ehrlich P(2012)The absolute arithmetic continuum and the unification of all numbers great and small Bull. Symbolic Logic 18 1-45
  • [3] Hahn H(1907)Über die nichtarchimedischen Grössensystem, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Mathematisch - Naturwiss Klasse (Wien) Abt. IIa 116 601-655
  • [4] Kuhlmann S(2011)Hardy type derivations on fields of exponential logarithmic series J. Algebra 345 171-189
  • [5] Matusinski M(2012)Hardy type derivations in generalized series fields J. Algebra 351 185-203
  • [6] Kuhlmann S(2005)-bounded exponential-logarithmic power series fields Ann. Pure Appl. Logic 136 284-296
  • [7] Matusinski M(2012)Comparison of exponential-logarithmic and logarithmic-exponential series Math. Logic Q. 58 434-448
  • [8] Kuhlmann S(2001)Fields of surreal numbers and exponentiation. Fund Math 167 173-188
  • [9] Shelah S(1997)Logarithmic-exponential power series J. London Math. Soc. 56 417-434
  • [10] Kuhlmann S(2001)Logarithmic-exponential series Proc. Int. Conf. Anal. Logique 111 61-113
12