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ON DEFINABLE SKOLEM FUNCTIONS IN WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

Published online by Cambridge University Press:  09 January 2018

PANTELIS E. ELEFTHERIOU ,
ASSAF HASSON  and
GIL KEREN
PANTELIS E. ELEFTHERIOU
Affiliation:
ZUKUNFTSKOLLEG AND DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF KONSTANZ BOX 216, 78457 KONSTANZ, GERMANYE-mail:panteleimon.eleftheriou@uni-konstanz.de
ASSAF HASSON
Affiliation:
DEPARTMENT OF MATHEMATICS BEN GURION UNIVERSITY OF THE NEGEV BE’ER SHEVA, ISRAELE-mail:hassonas@math.bgu.ac.il
GIL KEREN
Affiliation:
DEPARTMENT OF MATHEMATICS BEN GURION UNIVERSITY OF THE NEGEV BE’ER SHEVA, ISRAELE-mail:kerengi@cs.bgu.ac.il
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Abstract

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.

Keywords

03C64weakly o-minimal structuresdefinable Skolem functionso-minimal traces
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1482 - 1495
Copyright
Copyright © The Association for Symbolic Logic 2017 

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