TY - JOUR
T1 - ON LARGE EXTERNALLY DEFINABLE SETS IN NIP
AU - Bays, Martin
AU - Ben-Neria, Omer
AU - Kaplan, Itay
AU - Simon, Pierre
N1 - Publisher Copyright:
© The Author(s), 2023.
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 - 10.1017/S1474748023000464
DO - 10.1017/S1474748023000464
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AN - SCOPUS:85179053612
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 -