Gittin, Chapter 4, Mishnah 3. From this point until the end of the chapter, and also at the beginning of the next chapter, the Mishnah deals with matters that are not specifically related to gittin, but rather with enactments that the Sages instituted for the sake of tikkun ha'olam - measures taken in order to improve the state of the world.
The Enactment for the Widow: A Vow in Place of an Oath:
The Mishnah opens: "Ein almanah nifra'as minichsei yesomim ela bishevuah" - a widow may not collect her kesubah from the property of the orphans unless she first swears that she has not already collected any part of her kesubah.
However, "nimne'u mehashbi'ah" - they refrained from actually administering the oath to her, out of concern that she may indeed have collected part of the kesubah and would nevertheless be willing to swear that she had not, because she would justify it to herself, reasoning that what she took has nothing to do with the kesubah at all, but is rather payment rightfully due to her for the trouble and difficulty she went through in handling the affairs of the estate.
Rabbi Yehudah HaNasi therefore enacted "shetehei nodderes layesomim kol mah sheyirtzu vegovah kesubasah" - instead of an oath she takes a vow, that if she did in fact take from the kesubah, certain items will become forbidden to her and she will not benefit from them. Whatever vow the orphans ask her to take, she takes, and on that basis she collects her kesubah.
What is the logic behind this enactment?
An oath: a one-time act. A person convinces himself that it is justified, swears once, and the matter is over.
A vow: the prohibition against benefiting from certain items accompanies the one who vowed on an ongoing basis. The widow will encounter the prohibition again and again, and therefore it is less likely that she will take the vow unless it is completely true.
"Ha'edim chosmin al haget mipnei tikkun ha'olam":
Another enactment brought in the Mishnah is "ha'edim chosmin al haget mipnei tikkun ha'olam" - the signing of the witnesses on the get was instituted for the benefit of the world. Two approaches are offered in explaining this enactment:
The Mishnah was taught according to the view of Rabbi Eliezer, that the primary witnesses are the witnesses to the delivery - those who see the woman receive the get. For that reason an additional enactment was needed, that witnesses also sign on the get itself.
The Mishnah was taught according to the view of Rabbi Meir, that "the witnesses who sign effect the divorce" - the primary witnesses are those who sign the get. It was simply the practice not to write their full names, but only to write "witness," and the enactment came that they should write out their actual names.
The Enactment of the Prozbul:
The Mishnah concludes with the enactment of Hillel, who instituted the prozbul - this too was "mipnei tikkun ha'olam".
Loans are cancelled at the end of the shemittah year, the seventh year. Hillel saw that people were reluctant to lend money out of fear that they would lose their debt in shemittah, and in doing so they were transgressing the prohibition against refraining from lending. He therefore created this document: the lender transfers his debts to the court, and it is the court that collects the loans, and there is no prohibition against a court collecting debts after shemittah. This is a way of bypassing the cancellation of debts in the seventh year, and Hillel's enactment was meant to ensure that people would continue to lend money.
In summary: in this Mishnah we learned three enactments that were instituted for the sake of tikkun ha'olam: the vow that comes in place of the oath of a widow collecting her kesubah from the property of the orphans; the signing of the witnesses on the get, with its two approaches of explanation; and Hillel's enactment of the prozbul, which was meant to ensure that lending would continue even close to shemittah.