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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generic automorphisms of the universal partial order


Authors: D. Kuske and J. K. Truss
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
Published electronically: December 13, 2000
MathSciNet review: 1825900
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-00-05778-6
Keywords: Generic, partially ordered set, universal homogeneous, partial automorphism
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.
Article copyright: © Copyright 2000 American Mathematical Society