ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

Martin Bays; Omer Ben-Neria; Itay Kaplan; Pierre Simon

doi:https://doi.org/10.1017/S1474748023000464

ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

Martin Bays, Omer Ben-Neria, Itay Kaplan, Pierre Simon

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We study cofinal systems of finite subsets of. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.

Original language	English
Pages (from-to)	2159-2173
Number of pages	15
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	23
Issue number	5
DOIs	https://doi.org/10.1017/S1474748023000464
State	Published - 1 Sep 2024

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1017/S1474748023000464

Cite this

@article{4393b1b831ea40248d1a6a8e452fb77c,

title = "ON LARGE EXTERNALLY DEFINABLE SETS IN NIP",

abstract = "We study cofinal systems of finite subsets of. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.",

author = "Martin Bays and Omer Ben-Neria and Itay Kaplan and Pierre Simon",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2023.",

year = "2024",

month = sep,

day = "1",

doi = "https://doi.org/10.1017/S1474748023000464",

language = "الإنجليزيّة",

volume = "23",

pages = "2159--2173",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

number = "5",

}

TY - JOUR

T1 - ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

AU - Bays, Martin

AU - Ben-Neria, Omer

AU - Kaplan, Itay

AU - Simon, Pierre

PY - 2024/9/1

Y1 - 2024/9/1

N2 - We study cofinal systems of finite subsets of. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.

AB - We study cofinal systems of finite subsets of. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: In an NIP theory, any uncountable externally definable set contains an infinite definable subset. A similar result holds for larger cardinals.

UR - http://www.scopus.com/inward/record.url?scp=85179053612&partnerID=8YFLogxK

U2 - https://doi.org/10.1017/S1474748023000464

DO - https://doi.org/10.1017/S1474748023000464

M3 - مقالة

SN - 1474-7480

VL - 23

SP - 2159

EP - 2173

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 5

ER -

ON LARGE EXTERNALLY DEFINABLE SETS IN NIP

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this