u/wumbo52252

I was looking through the forcing section of a set theory book when I came to the part on boolean-valued models. When I was getting introduced to logic I remember wondering whether we should or would define models and satisfaction using algebras other than {0,1}. So seeing that done here caught my attention.

Are there other times when boolean-valued models, or something similar, are useful? I’m just curious—even if they’re not strictly necessary to get things done, as is the case with set-theoretic forcing.