2016/06/16 by Sano, Katsuhiko, Virtema, Jonni
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1606.05140
Let ML(U+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the relative definability of ML(U+) relative to finite transitive frames in the spirit of the well-known Goldblatt-Thomason theorem. We show that a class F of Kripke frames is definable in ML(U+) relative to finite transitive frames if and only if F is closed under taking generated subframes and bounded morphic images. In addition, we study modal definability in team-based logics. We study (extended) modal dependence logic, (extended) modal inclusion logic, and modal team logic. With respect to global model definability we obtain a trichotomy and with respect to frame definability a dichotomy. As a corollary we obtain relative Goldblatt--Thomason -style theorems for each of the logics listed above.