Hunter's Metalogic: An Introduction to the Metatheory of Standard First-Order Logic is not a "Math-popularization" book. You really need to be careful about your claims. It is a "book from another field" specifically philosophy. Again, you objection seems to be based on the idea that there is no difference between formal language and formal language (logic). I AGREE. I also believe that Theory and Theory (mathematical logic) are the same, and yet there are two articles. These splits are the result of politics not academics. Now I realize that we shouldn't have splits because of politics. You are going to have to talk to your mathematical brethren about not being so political. I am sorry, but that is the pragmatic reality. If legitimate content is repeatedly removed, then either it must stop, or there must be a way to save the content from the politics.