A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid.

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Title: A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid.
Author(s): 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.
Publication 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
Embargo Date: 2019-03-21
Appears in Collections:Pure Mathematics
Mathematics



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