(Mishnah - R. Eliezer): If a man divorced his wife, and said 'you are permitted to any man, Ela (but not) to Ploni', she is permitted [to all other men];

Chachamim forbid [her to all men; she is not divorced at all.

What does he do? He must take the Get and give it again, and say 'you are permitted to all men.'

If he wrote (the Tanai) in the Get, even if he returned and erased [the Tenai, the Get] is Pasul.

(Gemara - R. Ili): R. Eliezer learns from "v'Yatz'ah mi'Beiso v'Halchah v'Haysah l'Ish Acher" - even if he permitted her only to one man (it is a Get).

Objection: The Amora teaches more than the Mishnah! The Mishnah teaches [that it is a Get] when he permitted her to all, and forbade her only to one man. The Amora teaches when he forbade her to all, and permitted her only to one man! (If it is true, the Mishnah should have taught this. Do not say that the Mishnah taught when he forbids only to one, to teach that even then, Chachamim disqualify. It is better to teach Ko'ach d'Hetera, i.e. the extremity of the lenient opinion!)

Question: Rather, what is R. Eliezer's reason?

Answer: Death permits, and a Get permits (a Hekesh equates them). Just like death permits partially (she is still forbidden to her husband's relatives), also a Get permits partially.

Note: There is no limit how many brothers and sons her husband can have. He could have thousands, e.g. if he or his father had 1000 wives... We should learn that also a Get can leave thousands of men forbidden! However, there is no source to say that it can permit a limited number of men. (PF)

Question: What is Rabanan's reason?

Answer: "V'Yatz'ah mi'Beiso v'Halchah v'Haysah l'Ish Acher" equates her divorce to her Havayah (Kidushin). Just like her Kidushin cannot [exclude anyone, and] allow her to have Kidushin [also] with someone else, also her divorce [cannot exclude anyone].