Modal-Epistemic Arithmetic and the problem of quantifying in

The subject of this article is Modal-Epistemic Arithmetic, a theory introduced by Horsten to interpret Epistemic Arithmetic, which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret Modal-Epistemic Arithmetic in Epistemic Arithmetic and I will show how to get rid of a particular Platonist assumption. Then I will discuss models for Modal-Epistemic Arithmetic in light of the problems of logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution.