Presentability of groups of Σ-definable permutations over admissible sets

被引：0
作者：
Morozov A.S.
机构：
来源：
Algebra and Logic | 2002年 / 41卷 / 4期
关键词：
Admissible set; Group; Locally countable; Recursively listed; Σ-definability; Σ-definable (-presentable) permutation;
D O I：
10.1023/A:1020108705365
中图分类号：
学科分类号：
摘要：
It is proved that a group of all Σ-permutations of an arbitrary locally countable, recursively listed, admissible set is not Σ-presentable over that set. An example is constructed showing that this group can be presentable provided that the condition of being locally countable is dropped. © 2002 Plenum Publishing Corporation.
引用
收藏
页码：254 / 266
页数：12
相关论文
共 6 条
  • [1] Nurtazin A.T., On constructive groups, Proc. IV All-Union Conf. Math. Logic, (1976)
  • [2] Ershov Yu.L., Definability and Computability, (1996)
  • [3] Ershov Yu.L., Goncharov S.S., Constructive Models, (1999)
  • [4] Barwise J., Admissible Sets and Structures, (1975)
  • [5] Devlin K.J., Constructibility, Persp. Math. Log., (1984)
  • [6] Barwise J., Back and forth through infinitary logic, Studies in Model Theory, MAA Stud. Math., 8, pp. 5-34, (1973)
1