Explanation of the author's (may Allah have mercy on him) statement: "… and the letters of oath, which are: waw, ba, and ta …"

The Shaykh : The letters of oath, if they are found with a noun, if a word is entered by the letters of oath, it is a noun. The letters of oath also decline; they are from the letters of genitive case, which are waw, ba, and ta. These are the letters of oath. As for waw, Allah the Exalted said: al-Fajr. This is a noun because the letter of oath entered it. And in it is a second sign: alif and lam. And in it is a third: the genitive case.
Now, as for ba, Allah the Exalted said: Here, Allah is a noun because the letter of genitive case entered it. Do not follow me in error and correctness. If I make a mistake, say "error." Is here a letter of oath?
The student: ...

The Shaykh : It is not a letter of oath. It is not a letter of oath. Therefore, the ba here is a letter of genitive case, not a letter of oath.
The student: An oath.

The Shaykh : The ba here is a letter of oath. And Allah, this word is a noun. It is a noun in which are signs of a noun: the entry of the letter of oath upon it, the genitive case, alif and lam, and ta. The noun "Allah" is a noun, why? Because it has signs of a noun: the ta that is a letter of oath entered it, and it has alif and lam, which is one of the signs of a noun, and it has the genitive case, which is one of the signs of a noun. If we add the three letters of oath to the nine letters of genitive case, the total becomes twelve letters, all of which cause the genitive case. Now, the author (may Allah have mercy on him) mentioned ba in the letters of genitive case and in the letters of oath, so it is shared between the letters of genitive case and the letters of oath. The discussion on nouns is now finished. So a noun is known by four signs: the genitive case, tanwin, the entry of alif and lam, and the letters of genitive case. That means any word in which you find one of these signs is a noun. Sometimes two signs may gather in it, sometimes three signs may gather in it, and sometimes four signs may gather in it.
The student: No.

The Shaykh : No, why?
The student: ...

The Shaykh : Because tanwin and alif and lam do not gather. So it is three out of four. Yes, and Allah knows best.