Representation Embeddings of Cartesian Theories

Michael Lambert

Published 2016-12-08Version 1

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves indecomposable projective models and that preserves and reflects certain epimorphisms. This recalls standard definitions in the representation theory of associative algebras. The main result of this paper is that a representation embedding in the general sense preserves undecidability of theories. This result is applied to obtain an affirmative resolution of a reformulation in cartesian logic of a conjecture of M. Prest that every wild algebra over an algebraically closed field has an undecidable theory of modules.