11
IRUS TotalDownloads
Altmetric
A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid.
File | Description | Size | Format | |
---|---|---|---|---|
1510.00356.pdf | Accepted version | 225.26 kB | Adobe PDF | View/Open |
Title: | A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid. |
Authors: | Bodirsky, M Evans, D Kompatscher, M Pinsker, M |
Item 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. |
Issue Date: | 1-Apr-2018 |
Date of Acceptance: | 27-Jun-2016 |
URI: | http://hdl.handle.net/10044/1/61078 |
DOI: | https://dx.doi.org/10.1007/s11856-018-1645-9 |
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 |
Keywords: | 0101 Pure Mathematics General Mathematics |
Publication Status: | Published |
Appears in Collections: | Pure Mathematics Mathematics |