On notions of genericity and mutual genericity

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.