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September 2007 On notions of genericity and mutual genericity
J. K. Truss
J. Symbolic Logic 72(3): 755-766 (September 2007). DOI: 10.2178/jsl/1191333840

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.

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J. K. Truss. "On notions of genericity and mutual genericity." J. Symbolic Logic 72 (3) 755 - 766, September 2007. https://doi.org/10.2178/jsl/1191333840

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

zbMATH: 1123.03022
MathSciNet: MR2354899
Digital Object Identifier: 10.2178/jsl/1191333840

Subjects:
Primary: 06A99 , 20B27

Keywords: generic automorphism , mutually generic , random graph , rationals

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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