Title: Boolean-valued Second-order Logic

Speaker: Daisuke Ikegami (Sun Yat-sen University) 

Time: 2025/12/05 (Friday) 15:10-18:00 

Location:  Room B114, Lee Shau Kee Humanities Buildings No.2 (李兆基人文学苑2号楼), Peking University 

Abstract: 

In this talk, we introduce Boolean-valued second-order logic and compare it with full second-order logic (i.e., second-order logic with full semantics or Tarski semantics) on the following aspects: (1) the complexity of the validity, (2) compactness number, (3) Hanf number, (4) Löwenheim–Skolem number, and (5) the inner model constructed from the logic. We clarify the contexts where Boolean-valued second-order logic is much simpler than full second-order logic on the above aspects. This talk contains a joint work with Jouko Väänänen.