So, I recently started learning about modal logic, and thus also Possible Worlds semantics.
The formulation for a frame I was given is:
A frame is defined as an ordered pair $[G,R]$ where $G$ is the non-empty set of possible worlds, and $R$ is a relation $R \subseteq G \times G$.
So, it's obvious that this formulation uses set theoretic notions, but is this necessary? Are there formulations of modal logic that don't require set theory?