Introduction Millikan’s theory of content places great reliance on the existence of isomorphisms between a system of representations and the things in the world which they represent — “the mapping requirement for being intentional signs” (Millikan 2004, p. 106). This paper asks whether those isomorphisms are doing any substantive explanatory work. Millikan’s isomorphism requirement is deployed ...

Abstract We consider two inclusions of $C^{*}$ -algebras whose small have approximate units the large and their spaces all bounded bimodule linear maps. suppose that are strongly Morita equivalent. In this paper, we shall show there exists an isometric isomorphism from one maps to other space study basic properties about isomorphism. And, using isomorphism, define Picard group for a map discuss...

We investigate the back-and-forth types which isomorphism types. The main result is that the indecomposable isomorphism types which arise at the finite levels of the back-and-forth hierarchy are the same the finitary isomorphism types in Heindorff.

We consider the Boolean constraint isomorphism problem, that is, the problem of determining whether two sets of Boolean constraint applications can be made equivalent by renaming the variables. We show that depending on the set of allowed constraints, the problem is either coNP-hard and GI-hard, equivalent to graph isomorphism, or polynomial-time solvable. This establishes a complete classifica...

We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs, and determine for which first-order languages the isomorphism problem f...