ON DEFINABLE SKOLEM FUNCTIONS in WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

Pantelis E. Eleftheriou; Assaf Hasson; Gil Keren

doi:10.1017/jsl.2017.28

ON DEFINABLE SKOLEM FUNCTIONS in WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

Pantelis E. Eleftheriou, Assaf Hasson, Gil Keren

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	1482-1495
Number of pages	14
Journal	Journal of Symbolic Logic
Volume	82
Issue number	4
DOIs	https://doi.org/10.1017/jsl.2017.28
State	Published - 1 Dec 2017

Keywords

definable Skolem functions
o-minimal traces
weakly o-minimal structures

ASJC Scopus subject areas

Philosophy
Logic

Access to Document

10.1017/jsl.2017.28

Cite this

@article{7b5d62cf16944dee9c0928e332e3ddc7,

title = "ON DEFINABLE SKOLEM FUNCTIONS in WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES",

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 = "definable Skolem functions, o-minimal traces, weakly o-minimal structures",

author = "Eleftheriou, {Pantelis E.} and Assaf Hasson and Gil Keren",

note = "Publisher Copyright: Copyright {\textcopyright} The Association for Symbolic Logic 2017.",

year = "2017",

month = dec,

day = "1",

doi = "10.1017/jsl.2017.28",

language = "English",

volume = "82",

pages = "1482--1495",

journal = "Journal of Symbolic Logic",

issn = "0022-4812",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - ON DEFINABLE SKOLEM FUNCTIONS in WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

AU - Eleftheriou, Pantelis E.

AU - Hasson, Assaf

AU - Keren, Gil

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - definable Skolem functions

KW - o-minimal traces

KW - weakly o-minimal structures

UR - http://www.scopus.com/inward/record.url?scp=85040441461&partnerID=8YFLogxK

U2 - 10.1017/jsl.2017.28

DO - 10.1017/jsl.2017.28

M3 - Article

AN - SCOPUS:85040441461

SN - 0022-4812

VL - 82

SP - 1482

EP - 1495

JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

IS - 4

ER -

ON DEFINABLE SKOLEM FUNCTIONS in WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this