A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid.
File(s)
Accepted version
Author(s)
Bodirsky, M
Evans, D
Kompatscher, M
Pinsker, M
Type
Journal Article
Abstract
© 2018, Hebrew University of Jerusalem. We present an example of two countable ω-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids—in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable ω-categorical structure in a finite relational language which can neither be reconstructed up to first-order biinterpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone.
Date Issued
2018-04-01
Date Acceptance
2016-06-27
Citation
Israel Journal of Mathematics, 2018, 224 (1), pp.57-82
ISSN
0021-2172
Publisher
Springer Verlag
Start Page
57
End Page
82
Journal / Book Title
Israel Journal of Mathematics
Volume
224
Issue
1
Copyright Statement
© 2018 Springer-Verlag. The final publication is available at Springer via https://dx.doi.org/10.1007/s11856-018-1645-9
Subjects
0101 Pure Mathematics
General Mathematics
Publication Status
Published