Dzhaparidze, G. (1993), A generalized notion of weak interpretability and the corresponding modal logic

The paper can be downloaded from here, here I collect some comments on it. This is one of the sources I use to connect my B.A. Philosophy Thesis to the literature. I will therefore often make comparisons with my work and definitions.

Introduction

There are two definitions from the past papers by Tarski that are relevant here:

For theories $T$ and $S$ we say ”$T$ interprets $S$” if there is a translation $\tau :{\mathcal{L}}_S\to {\mathcal{L}}_T$ s.t. ${\forall }_{\phi \in {\mathcal{L}}_S}S⊢\phi \to T⊢\tau (\phi )$. This exactly resembles my notion of Partial Translation of the theory $T$. Here what I call Logic are called “Languages”.

Before proceeding I switch to studying: