Definable choice for a class of weakly o-minimal theories

被引：2
|
作者：
Laskowski, Michael C. [1 ]
Shaw, Christopher S. [2 ]
机构：
[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA
[2] Columbia Coll Chicago, Dept Sci & Math, 600 S Michigan Ave, Chicago, IL 60605 USA
来源：
ARCHIVE FOR MATHEMATICAL LOGIC | 2016年 / 55卷 / 5-6期
关键词：
Weakly o-minimal; Skolem functions; Definable choice; ORDERED STRUCTURES; TAME EXTENSIONS; T-CONVEXITY; SETS; PAIRS;
D O I：
10.1007/s00153-016-0490-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an o-minimal structure with a group operation, we show that for a properly convex subset U, the theory of the expanded structure has definable Skolem functions precisely when is valuational. As a corollary, we get an elementary proof that the theory of any such does not satisfy definable choice.
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页码：735 / 748
页数：14
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