Degrees of Kripke Incompleteness (2024)

Individual MoL project, May 2024, ILLC.

Instructors: Rodrigo N. Almeida, Qian Chen and Nick Bezhanishvili

Project Description

Kripke-completeness of modal logics has been extensively studied since 1960s. Fine raised a question concerning the degree of Kripke-incompleteness of logics in the lattice of all normal modal logics. In this project, we mainly focus on degree of incompleteness of modal logic and the proof of Blok’s dichotomy theorem: every modal logic is of the degree of Kripke-incompleteness 1 or continuum.

References

• Alexander Chagrov and Michael Zakharyaschev, (1968) Modal Logic.
• W. J. Blok, (1978) On the Degree of Incompleteness of Modal Logics (Abstract). Bulletin of the Section of Logic, 7(4):167–172.