# Boolean-valued second-order logic

Daisuke Ikegami, Jouko Väänänen

2 引用 (Scopus)

### 抄録

In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its validity is absolute under forcing, and its Hanf and Löwenheim numbers are smaller than those of full second-order logic.

元の言語 English 167-190 24 Notre Dame Journal of Formal Logic 56 1 https://doi.org/10.1215/00294527-2835065 Published - 2015 1 1 Yes

• Logic

### これを引用

Boolean-valued second-order logic. / Ikegami, Daisuke; Väänänen, Jouko.

：: Notre Dame Journal of Formal Logic, 巻 56, 番号 1, 01.01.2015, p. 167-190.

Ikegami, Daisuke ; Väänänen, Jouko. / Boolean-valued second-order logic. ：: Notre Dame Journal of Formal Logic. 2015 ; 巻 56, 番号 1. pp. 167-190.
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