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On notions of genericity and mutual genericity

Published online by Cambridge University Press:  12 March 2014

J. K. Truss
J. K. Truss*
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England, UK. E-mail: pmtjkt@leeds.ac.uk
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Abstract

Generic automorphisms of certain homogeneous structures are considered, for instance, the rationals as an ordered set, the countable universal homogeneous partial order, and the random graph. Two of these cases were discussed in [7], where it was shown that there is a generic automorphism of the second in the sense introduced in [10], In this paper, I study various possible definitions of ‘generic’ and ‘mutually generic’, and discuss the existence of mutually generic automorphisms in some cases. In addition, generics in the automorphism group of the rational circular order are considered.

Keywords

generic automorphismmutually genericrationalsrandom graph
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 755 - 766
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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