Generic automorphisms of the universal partial order
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- by D. Kuske and J. K. Truss PDF
- Proc. Amer. Math. Soc. 129 (2001), 1939-1948 Request permission
Abstract:
We show that the countable universal-homogeneous partial order $(P,<)$ has a generic automorphism as defined by the second author, namely that it lies in a comeagre conjugacy class of Aut$(P,<)$. For this purpose, we work with ‘determined’ partial finite automorphisms that need not be automorphisms of finite substructures (as in the proofs of similar results for other countable homogeneous structures) but are nevertheless sufficient to characterize the isomorphism type of the union of their orbits.References
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Additional Information
- D. Kuske
- Affiliation: Institut für Algebra, Technische Universität Dresden, D-01062 Dresden, Germany
- Address at time of publication: Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, England
- Email: kuske@math.tu-dresden.de, D.Kuske@mcs.le.ac.uk
- J. K. Truss
- Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England
- Email: pmtjkt@leeds.ac.uk
- Received by editor(s): September 14, 1999
- Received by editor(s) in revised form: November 15, 1999
- Published electronically: December 13, 2000
- Additional Notes: Research supported by a grant from the British-German Academic Collaboration Programme. The authors thank the referee for helpful suggestions.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1939-1948
- MSC (2000): Primary 06A06, 20B27
- DOI: https://doi.org/10.1090/S0002-9939-00-05778-6
- MathSciNet review: 1825900