MODNET
Research Training Network in Model Theory
 Publications > Preprint server > Preprint Number 936 Preprint Number 936 936. Manuel Bodirsky, David Evans, Michael Kompatscher, Michael Pinsker A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoids E-mail: (email address protected by JavaScript. Please enable JavaScript to contact) Submission date: 1st October 2015. Abstract: 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 $\omega$-categorical structure in a finite relational language which can neither be reconstructed up to first-order bi-interpretations 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. Mathematics Subject Classification: Keywords and phrases: Full text arXiv 1510.00356: pdf, ps.

 Last updated: October 8 2015 13:09 Please send your corrections to: The e-mail address is protected, enable Javascript to see it