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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the countable universal-homogeneous partial order has a generic automorphism as defined by the second author, namely that it lies in a comeagre conjugacy class of Aut. 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