  As Tarski and others have pointed out, the permutation invariance criterion for logical constants can be seen as a natural generalization of Felix Klein’s (1893) idea that different geometries can be distinguished by the groups of transformations under which their basic notions are invariant. Thus, for example, the notions of Euclidean geometry are invariant under similarity transformations, those of affine geometry under affine transformations, and those of topology under bicontinuous transformations. In the same way, Tarski suggests (1986, 149), the logical notions are just those that are invariant under the widest possible group of transformations: the group of permutations of the elements in the domain. Seen in this way, the logical notions are the end point of a chain of progressively more abstract, “formal,” or topic-neutral notions defined by their invariance under progressively wider groups of transformations of a domain.[13]