Journal of Symbolic Logic

On notions of genericity and mutual genericity

J. K. Truss

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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.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 3 (2007), 755-766.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333840

Digital Object Identifier
doi:10.2178/jsl/1191333840

Mathematical Reviews number (MathSciNet)
MR2354899

Zentralblatt MATH identifier
1123.03022

Subjects
Primary: 20B27: Infinite automorphism groups [See also 12F10] 06A99: None of the above, but in this section

Keywords
generic automorphism mutually generic rationals random graph

Citation

Truss, J. K. On notions of genericity and mutual genericity. J. Symbolic Logic 72 (2007), no. 3, 755--766. doi:10.2178/jsl/1191333840. https://projecteuclid.org/euclid.jsl/1191333840


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