Gemara

12a (Shmuel): If one was Mekadesh with a date, even if it sells for far less than a Perutah, we are concerned lest it is worth a Perutah in Madai (elsewhere).

Question (Mishnah - Beis Hillel): A Perutah or Shavah Perutah is Mekadesh.

Inference: Less than a Shavah Perutah is not Mekadesh!

Answer: A Perutah makes Vadai (definite) Kidushin. Less than a Perutah creates Safek (doubtful) Kidushin.

Reuven was Mekadesh Leah with a piece of marble. Rav Chisda was calculating whether it is worth a Perutah.

Question: Shmuel taught that even if it is not worth a Perutah, we are concerned!

Answer: Rav Chisda argues with Shmuel.

Leah's mother said that on the day that he was Mekadesh her, it was worth a Perutah. Rav Chisda said that she is not believed (to forbid her to his brother Shimon, who was Mekadesh her after Reuven).

Rav Chisda heard about witnesses abroad who say that the rock was worth a Perutah that day. He said 'since they are not here, we are not concerned.'

(Abaye and Rava): We cannot be lenient. Perhaps the rumors are true!

Leah married someone else. Chachamim of Sura would not marry her children.

This is not because they hold like Shmuel. They hold like Abaye and Rava.

(Rav Yosef): If one was Mekadesh with a myrtle branch, she is Safek Mekudeshes, like Shmuel taught.

Shimon was Mekadesh Rachel with a myrtle mat. Onlookers said that it is not worth a Perutah! Shimon said that she should be Mekudeshes with the four Zuzim inside. Rachel took it and was silent.

(Rava): Silence after the money was already given has no effect.

Question (Chachamim of Fum Nahara, citing Rav Huna brei d'Rav Yehoshua): If she does not want to be Mekudeshes, she should throw it back!

Answer (Rav Achai): Perhaps she fears lest it get lost, and she will need to pay!

(Ravina): We never heard Rav Huna's question, so we rule like Rava (she is not Mekudeshes); You (in Fum Nahara) heard his question. You must be stringent!

Rishonim

The Rif brings the Gemara verbatim.

Ran (DH umid'Amrinan): The Ro'oh says that we are concerned for rumors of witnesses (who know that it was worth a Perutah) only if the rumors preceded the second Kidushin. Bahag rules unlike Shmuel, for the Gemara said that Rav Chisda and those who argue with him disagree with Shmuel. Others dispel the proof; Rabanan were stringent not only due to Shmuel, rather, also due to Abaye and Rava. The Gemara connotes otherwise.

Note: It seems that the Ro'oh rules unlike Shmuel. Even without rumors she is Safek Mekudeshes to the first man! Alternatively, he holds that Shmuel's law is a mere stringency, so surely we force the first man to divorce her. If we were concerned for the rumors, the second man should divorce her!

Rambam (Hilchos Ishus 4:19): If one was Mekadesh with a food, Kli, etc. worth less than a Perutah, she is Safek Mekudeshes. She needs a Get, lest it is worth a Perutah elsewhere. If one was Mekadesh with a perishable cooked food, vegetable, etc., if it is not worth a Perutah in that place, she is not Mekudeshes at all, for it will perish before she brings it elsewhere. One may rely on this.

Ran (DH Omar, citing Tosfos): Shmuel decreed lest someone from Madai see that Kidushin with this item is invalid, and will not be concerned for such Kidushin in Madai. This applies to even to perishables.

Rosh (1:17): Shmuel's law is a stringency mid'Rabanan. Mid'Oraisa, (redemption of) Hekdesh depends only on (the value in) that time and place. The same applies to monetary laws. The Gemara says 'Kidushei Safek', but really, it is Kidushin mid'Rabanan. They made it like a Safek. She is not permitted without a Get. The Mekadesh must give her Vadai Kidushin (if he wants to keep her). The Ri says that even if we know that it is worth a Perutah elsewhere, Hekdesh depends on only that time and place. Shmuel taught a Chidush that we are stringent even when we do not know that it is worth a Perutah anywhere. Chachamim decreed due to where it is Shavah Perutah. This applies even if it is perishable. Presumably, the Ri is correct. A woman does not acquire herself to a man for something not Shavah Perutah where she lives.

Poskim

Shulchan Aruch (EH 31:3): If Reuven was Mekadesh Leah a food, etc. not worth a Perutah, she is Safek Mekudeshes. Perhaps it is worth a Perutah elsewhere.

Beis Yosef (DH u'Mah she'Chosav v'Im): The Rif, Rambam and Rosh rule like Shmuel. The Ge'onim, Ramban and Rashba agree (Magid Mishneh).

Note: The Rif brings the Sugya verbatim. However, if the Hagahah (see Bach 5) is not from the Rif, he brings Shmuel's opinion, but not those who argue.

Beis Shmuel (6): Since it is not Shavah Perutah here, this Kidushin has no witnesses! Rather, since the witnesses have this Safek, it is Safek Kidushin.

Shulchan Aruch (ibid.): Some say that if he was Mekadesh with a perishable cooked food, vegetable, etc., if it is not worth a Perutah in that place, she is not Mekudeshes at all, for it will perish before she brings it elsewhere.

Beis Yosef (DH Kosav Maharik): If one can cause a perishable food to last, e.g. a date can be dried out, it is like a food that lasts.

Shulchan Aruch (4): Leah is Safek Mekudeshes lest it is Shavah Perutah elsewhere. She needs a Get to permit her to others. If Reuven wants to keep her, he must give her Vadai Kidushin. If Levi was Mekadesh her Vadai, Reuven gives a Get and Levi can marry her. If Levi gave a Get, Reuven may not marry her.

Chelkas Mechokek (10): If also Levi was Mekadesh her with less than Shavah Perutah, she may get a Get from either and marry the other.

Beis Shmuel (8): If Levi was Mekadesh her with the same item, she is permitted to Reuven without a Get from Levi, for if it was worth a Perutah somewhere, she was already Mekudeshes to Reuven.

Beis Shmuel (9): According to those who say that the Kidushin is only mid'Rabanan, she could marry Reuven after Levi gives a Get. However, perhaps we forbid lest people (in whose land it is Shavah Perutah) think that one may remarry his divorcee even if the Kidushin was mid'Oraisa.

Rema: If Levi had Bi'ah with her before Reuven divorced her, she becomes forbidden to Reuven, and also to Levi.

Beis Shmuel (10): Maharik (84:3) forbids even if a Chacham ruled that she is permitted. The Rashba (1189) permits one who followed a Chacham's ruling. However, he himself gives ways to dispel his proof.

Shulchan Aruch (ibid.): Some say that if Reuven did not divorce her and she had a child from Levi, the child is Kosher.

Chelkas Mechokek (11): The Ramah says so. The Beis Yosef says that he holds like the Ri, that it is a mere stringency to require a Get. We must say that the Rabanan who separated from the family were merely stringent. According to the Rambam, the child is a Safek Mamzer.

Gra (8): Bahag rules unlike Shmuel, for Rabanan separate from the family only due to Abaye and Rava. Also, a man was Mekadesh with a myrtle mat with coins inside; Ravina (13a) was concerned for the coins, but not for Shmuel's law). Most rule like Shmuel, for Rav Yosef agrees. They say that the man retracted from Kidushin with the mat, and wanted Kidushin only through the coins. According to those who Machshir the child, even if Rabanan held like Shmuel, they needed a different reason to be stringent.

Beis Shmuel (11): If there are rumors that it was Shavah Perutah, all agree that the child is a Safek Mamzer.