Commutativity and self-reference (Q786803)

A common occurrence in fixed point theory is the sharing of some fixed point by commuting operators. But, how common is (his occurrence in the arithmetical fixed point theory, i.e., in the theory of arithmetical self-reference? The author features the modal analysis of arithmetical self-reference as a tool to study this question and gives some observations with open problems from such a point of view. In the introduction, the author says: Though the results are not difficult, I think they do testify to the coherence of the modal theory. Moreover, through the exhibition of nontrivial differences between varying types of self-reference, they offer some indication of the possibility of a rich theory of arithmetical self-reference.