ON DEFINABLE SKOLEM FUNCTIONS IN WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

被引：6

作者：

Eleftheriou, Pantelis E. ^{[1
,2
]}

Hasson, Assaf ^{[3
]}

Keren, Gil ^{[3
]}

机构：

[1] Univ Konstanz, Zukunftskolleg, Box 216, D-78457 Constance, Germany

[2] Univ Konstanz, Dept Math & Stat, Box 216, D-78457 Constance, Germany

[3] Ben Gurion Univ Negev, Dept Math, Beer Sheva, Israel

来源：

JOURNAL OF SYMBOLIC LOGIC | 2017年 / 82卷 / 04期

基金：

以色列科学基金会;

关键词：

weakly o-minimal structures; definable Skolem functions; o-minimal traces; EXPANSIONS; PAIRS;

D O I：

10.1017/jsl.2017.28

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that all known examples of weakly o-minimal nonvaluational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up to definable families of cuts. Along the way we give some new examples of weakly o-minimal nonvaluational structures.

引用

下载

页码：1482 / 1495

页数：14

共 50 条

[31] On the Boolean algebras of definable sets in weakly o-minimal theories
Leonesi, S
Toffalori, C
MATHEMATICAL LOGIC QUARTERLY, 2004, 50 (03) : 241 - 248
[32] Rings of analytic functions definable in o-minimal structure
Fujita, M
Shiota, M
JOURNAL OF PURE AND APPLIED ALGEBRA, 2003, 182 (2-3) : 165 - 199
[33] DIRECTIONAL PROPERTIES OF SETS DEFINABLE IN O-MINIMAL STRUCTURES
Koike, Satoshi
Ta Le Loi
Paunescu, Laurentiu
Shiota, Masahiro
ANNALES DE L INSTITUT FOURIER, 2013, 63 (05) : 2017 - 2047
[34] HIGHER HOMOTOPY OF GROUPS DEFINABLE IN O-MINIMAL STRUCTURES
Berarducci, Alessandro
Mamino, Marcello
Otero, Margarita
ISRAEL JOURNAL OF MATHEMATICS, 2010, 180 (01) : 143 - 161
[35] Definable one dimensional structures in o-minimal theories
Assaf Hasson
Alf Onshuus
Ya’acov Peterzil
Israel Journal of Mathematics, 2010, 179 : 297 - 361
[36] DEFINABLE ONE DIMENSIONAL STRUCTURES IN O-MINIMAL THEORIES
Hasson, Assaf
Onshuus, Alf
Peterzil, Ya'acov
ISRAEL JOURNAL OF MATHEMATICS, 2010, 179 (01) : 297 - 361
[37] Transversality of smooth definable maps in O-minimal structures
Nhan Nguyen
Trivedi, Saurabh
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2020, 168 (03) : 519 - 533
[38] Diophantine properties of sets definable in o-minimal structures
Wilkie, AJ
JOURNAL OF SYMBOLIC LOGIC, 2004, 69 (03) : 851 - 861
[39] Topology of definable abelian groups in o-minimal structures
Baro, Elias
Berarducci, Alessandro
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2012, 44 : 473 - 479
[40] CARTAN SUBGROUPS OF GROUPS DEFINABLE IN O-MINIMAL STRUCTURES
Baro, Elias
Jaligot, Eric
Otero, Margarita
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2014, 13 (04) : 849 - 893

← 1 2 3 4 5 →