The Invariance Modality

In Gerla (1987), G. Gerla introduced the so-called transformational semantics for predicate modal logic and considered in particular semantic frame- works given by a classical model endowed with a group of automorphisms, where a boxed formula is true iff it holds invariantly (i.e. it remains true whenever an automorphism is applied to the individuals it is talking about). With this interpreta- tion, de dicto modalities collapse, but de re modalities remain quite informative. We handle the axiomatization problem of such modal structures, by employing classic model-theoretic tools (iterated ultrapowers and double chains).