EPPA for two-graphs and antipodal metric spaces
OA Location
Author(s)
Evans, David M
Hubicka, Jan
Konecny, Matej
Nesetril, Jaroslav
Type
Journal Article
Abstract
We prove that the class of finite two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching automorphisms. We present a short, self-contained, purely combinatorial proof which also proves EPPA for the class of integer-valued antipodal metric spaces of diameter 3, answering a question of Aranda et al.
The class of two-graphs is an important new example which behaves differently from all the other known classes with EPPA: Two-graphs do not have the amalgamation property with automorphisms (APA), their Ramsey expansion has to add a graph, it is not known if they have coherent EPPA, and even EPPA itself cannot be proved using the Herwig–Lascar theorem.
The class of two-graphs is an important new example which behaves differently from all the other known classes with EPPA: Two-graphs do not have the amalgamation property with automorphisms (APA), their Ramsey expansion has to add a graph, it is not known if they have coherent EPPA, and even EPPA itself cannot be proved using the Herwig–Lascar theorem.
Date Issued
2020-05-01
Date Acceptance
2020-01-01
Citation
Proceedings of the American Mathematical Society, 2020, 148 (5), pp.1901-1915
ISSN
0002-9939
Publisher
American Mathematical Society
Start Page
1901
End Page
1915
Journal / Book Title
Proceedings of the American Mathematical Society
Volume
148
Issue
5
Copyright Statement
© 2020 American Mathematical Society
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000521585500007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
EXTENDING PARTIAL ISOMORPHISMS
SMALL INDEX PROPERTY
GRAPHS
Publication Status
Published
Date Publish Online
2020-01-15