The Institution-Theoretic Scope of Logic Theorems

In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model theoretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of (Craig) interpolation and (Beth) definability, as they appear in the literature of institutional model theory. Both case studies illustrate a considerable extension of the original scopes of the two classical theorems. Our presentation is rather narrative with the relevant logic and institution theory concepts introduced and explained gradually to the non-expert reader. Mathematics Subject Classification (2010). Primary 03C95; Secondary 03C40, 03B70.