Saturated Models and Ultrafilter Extension for Weakly Aggregative Modal Logics

Studies in Logic, Vol. 17, No. 6 (2024): 76–92                 PII: 1674-3202(2024)-06-0076-17

Yifeng Ding, Jixin Liu

Abstract. Weakly aggregative modal logics (WAML) are a series of natural weakenings of the minimal modal logic K. The natural semantics for them are based on Kripke frames with an N + 1-ary relation, where □φ is true at a world iff all of its successor N-tuples has at least one world making φ true. We study the notion of saturated models and ultrafilter extension for this relational semantics of WAML. The Goldblatt-Thomason theorem for WAML is proved as an application.