This paper extends the theory of regions developed by Nielsen, Rozenberg and Thiagarajan within a set-theoretic framework, to accommodate the class of non-pure nets and their transition systems. Those are called semi-elementary nets and semi-elementary transition systems, respectively. The main motivation of such an extension is practical, the need to model asyn-chronous hardware structures, wh...

Abstract We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic {HA}$ . Using a generalized negative translation, we first provide structured proof the fact that is $\Pi _{k+2}$ -conservative over {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma axiom scheme law-of-excluded-middl...