Reading my logic textbook, I faced the following two sentences, of which I’m kind of confused.
(1) For given a formula A in Γ, take n so large that …
(2) ... in which P1 takes the value i(P1). For let Δ be a finite subset of Γ. Then ...
In (1), I thought it should have been “for a given formula ...” Isn’t this a normal order for such constructions? Any reason for that?
In (2), I don’t get it what that “for” is for. Was it used as a conjunction, by any chance?
P.S. I’m not sure if I have to put these questions in separate posts. Please let me know, then I’ll follow.
Edit: I attach the page.