User blog comment:DontDrinkH20/H-Boogol-Boogol Bit by bit: PART 1: Model Theory 101/@comment-35470197-20180901140237/@comment-35470197-20180901222314

> I didn't mean every theory

Oh, I see. Then ok.

> mathematics (those which can interpret arithmetic)

(And also are effectively axiomiesd)

> Good job pointing out typos, you are like an unpaid editor for me at this point :D

Haha. I just like to read your blog post very much, and would like also others to read them. Your blog post is really informative. But sorry if I am doing too much annoying comments :P

> Also, what do you mean by "typo of \(\forall v_n(\varphi))"?

I thought that you are explaining the following: Therefore I guessed that it is a typo of the following: I am sorry if I misunderstood what you intend.
 * 1) The formula "\(\forall v_n(\varphi)\)" is valid if and only if \(v_n\) is a free variable in \(\varphi). (Definition of the validity of quantification)
 * 2) The variable \(v_n\) is not a free variable in "\(\forall v_n(\varphi)\)" any more. (Definition of the free ocurrence of a variable)
 * If \(v_n\) is a "free variable" in \(\varphi\), then "\(\forall v_n(\varphi)\)" is a valid formula, and \(v_n\) is NOT a free variable of \(\forall v_n(\varphi)\). (for ever \(v_n\)...)