Gemara

(Beraisa): If a man gave to a woman money and said 'You are Mekudeshes to me', she is Mekudeshes;

If she gave (money to him) and said 'I am Mekudeshes to you', she is not Mekudeshes.

Question (Rav Papa): The Reisha implies that had (he given the money and) she said the words, she would not be Mekudeshes. The Seifa implies that had he given the money (and she said the words), she would be Mekudeshes!

Answer #1: If he gave the money and she said these words, it is as if she gave the money and said the words, and she is not Mekudeshes.

Answer #2: If he gave the money and she said the words, it is a Safek. Mid'Rabanan. We are stringent and consider her Safek Mekudeshes.

Rishonim

Rif and Rosh (Kidushin 2a and 1:1): If he gave the money and she said the words, we are concerned mid'Rabanan, and she needs a Get.

Ran (DH Tanu): The Gemara says 'it is a Safek, and mid'Rabanan we are concerned'. If it is a Safek, we should be concerned mid'Oraisa! The Rif omitted 'it is a Safek'. He holds that surely it is not Kidushin; mid'Rabanan we consider it a Safek. The Gemara connotes otherwise. The Rambam calls it Safek Kidushin; he does not say 'mid'Rabanan'. Perhaps no Safek Kidushin requires a Get mid'Oraisa, for we follow the Chazakah that she is single, just like every monetary Safek. All agree that if the other party seized the money in doubt, we return it to the Muchzak. The same applies to Safek Kidushin. Mid'Rabanan, we are stringent about Safek Ervah. Therefore we are concerned for every Safek Kidushin. However, elsewhere the Rif says 'it is a Safek Kidushin mid'Oraisa, and we are stringent.' This requires investigation.

Korban Nesan'el (30): It seems that the Gemara was unsure if we should establish the Beraisa like Answer #1 (it is as if she gave and spoke, and she is Vadai not Mekudeshes) or like Answer #2 (it is a Safek). Mid'Rabanan we are stringent like the latter answer.

Note: Perhaps mid'Oraisa we could be lenient because it is a Sefek-Sefeka.

Rambam (Hilchos Ishus 3:2): If he gave the money and she said the words, she is Mekudeshes mi'Safek.

Magid Mishnah: This is like the Answer #2; we are concerned mid'Rabanan.

Rambam (Hilchos Gerushin 10:3): Whenever I say that there is Safek Gerushin, if she remarried she must leave. The child is a Safek Mamzer. If she did not remarry, her ex-husband may remarry her without a new Nisu'in, Sheva Berachos and Kesuvah. These are needed only after Vadai Gerushin.

Maharik (172, brought in Kesef Mishneh): If she remarried after Safek Kidushin, the Rambam did not say that she must leave and the child is a Safek Mamzer, for she is Muchzekes to be is single. In Safek Gerushin, she is Muchzekes to be married. If she remarried, she must leave and the child is a Safek Mamzer. For the same reason, the Rambam requires new Kidushin after Safek Kidushin, but not after Safek Gerushin.

Rosh: This is when he was not discussing Kidushin with her. If he was, she is Mekudeshes even if he gave the money in silence. Her words do not detract.

Me'iri (5b DH Ikar): The Rambam holds that even a Safek Torah is forbidden only mid'Rabanan. Some say that even if he was discussing Kidushin with her, if she did the Amirah, it is Safek Kidushin. Her speech is worse than silence, for he relies on it. This is wrong. It is no worse than if he gave and spoke, and she also spoke. We do not need her words, so they do not harm.

Tosfos Rid (6a DH Iy): Even if he was discussing Kidushin with her, if she did the Amirah, it is not full Kidushin. It seems that the Kidushin finished with her words. It must conclude with his words.

Poskim

Shulchan Aruch (EH 27:8): If he gave the money and she said the words, if he was speaking about Kidushin with her, she is Vadai Mekudeshes. If not, she is Mekudeshes mi'Safek.

Beis Yosef (DH u'Mah she'Chosav Od): Why does the Tur say that the Rambam is a Chidush? Surely he agrees that if they were discussing Kidushin, her Dibur does not hurt, and she is Vadai Mekudeshes!

Ran (ibid. and 3a DH Ten): When he gave the money and said the words, and she was quiet, her silence is consent to his words. Perhaps when he gave the money and she said the words, and he was quiet, his silence is consent to her words, and it is as if he was discussing Kidushin with her. Her silence is more conclusive, for she becomes forbidden to all men. His silence does not forbid him, so perhaps he is not concerned to express his refusal!

Ran (3a DH Ten): If Leah told Reuven 'give money to Ploni, and I will be Mekudeshes to you' she is Mekudeshes (6b). The case is, he said 'you are Mekudeshes to me through my gift to Ploni.' Some say that he was quiet, and his silence was consent to her words. This is wrong. It is a Safek whether his silence is considered "a man will take a woman". If she spoke after he gave and he was quiet, this is no better than when he gave and later spoke. Her silence does not help at all (12b)!

Beis Shmuel (22): The Rif, Rosh, Ran and R. Yerucham say that it is a mere stringency mid'Rabanan.

Question (Be'er Heitev 25): Tosfos (5b DH Ha, and the Rosh) say that the Gemara did not discuss when she gave and he spoke, for the law is not uniform. If he is esteemed (receiving from her is like giving to her, so) she is Mekudeshes. This implies that when he gave and she spoke, she is Safek Mekudeshes in every case, even if they were discussing Kidushin! See the Rosh (he explicitly says otherwise)!

Erech Lechem: Ben Lev says that if she was speaking about Kidushin with him, she is Safek Mekudeshes.

Shulchan Aruch (ibid.): If (he gave and she spoke, and) he answered 'Hen (yes)', it is Vadai Kidushin, even if they were not discussing Kidushin.

Chelkas Mechokek (20): The Bach says that if they were not discussing Kidushin, it is Safek Kidushin, for 'Hen' can mean 'no'.

Rebuttal (Beis Shmuel 23): If one was Mekadesh with something he stole from her and she said 'Hen', it is Kidushin (Vadai - 28:2)! Also the Drishah cites the Maharshal who agrees with the Shulchan Aruch.