Sotah chapter 6, mishnah 1. This mishnah presents another version of the dispute between Rabbi Eliezer and Rabbi Yehoshua that was already taught at the beginning of chapter 1: according to Rabbi Eliezer, although the warning (kinui) must be given in the presence of two witnesses, the seclusion itself need not be witnessed by valid witnesses, and a single witness suffices, even the husband himself. Rabbi Yehoshua, on the other hand, holds that the seclusion too requires two witnesses.
The view of Rabbi Eliezer:
The mishnah opens: "Mi shekinei l'ishto v'nisterah" - he warned her in the presence of two witnesses, and after the warning she secluded herself, but there are no valid witnesses to the seclusion. "Afilu shama me'of haporeach" - literally, even if he heard it from a flying bird, a figurative expression for testimony that is not valid, such as a single witness; and nevertheless, according to Rabbi Eliezer, based on the mishnah in the first chapter, the husband may bring her up to Jerusalem and have her drink the waters of the sotah on that basis.
But for whatever reason the husband decided that he does not wish to do so, and he is therefore in the category of a husband who says, "I will not have her drink." In such a situation - "yotzi v'yiten ketubah": he must divorce her, since she is not drinking, and it is the drinking that would permit her to him; and he must pay her ketubah, since he is the one refusing to have her drink, and according to his own view she could have drunk even on the strength of the testimony of the "flying bird," that is, a witness who is not valid. "Divrei Rabbi Eliezer" - these are the words of Rabbi Eliezer.
The view of Rabbi Yehoshua:
Rabbi Yehoshua, who holds that the seclusion requires two valid witnesses, maintains that when there are no valid witnesses - and this is the case the mishnah is dealing with, where all we have is a "flying bird," a witness who is not trustworthy - the woman is not forbidden to her husband on the basis of testimony that is not valid. She becomes forbidden only if matters have reached the point where the women who spin wool by moonlight are talking about her disgrace.
Spinning wool by moonlight was work that women would do together, and while doing it they would talk with one another and gossip. Once matters have reached the level where the women regularly gossip about her improper behavior, the situation is ugly enough that the husband cannot keep her as his wife. And not only that, but according to Rabbi Yehoshua's understanding, even the waters of the sotah are of no help to her, as we learn from the verse.
Therefore she is not formally forbidden to him, but he is obligated to divorce her once her behavior has reached this level, and even so he must pay her ketubah, since nothing has actually been proven; it is only that matters have become so ugly that it is not fitting for them to remain married to one another.
In summary: in this mishnah Rabbi Eliezer and Rabbi Yehoshua disagree about the level of testimony required regarding the seclusion. According to Rabbi Eliezer, even a "flying bird" suffices, and once the husband is unwilling to have her drink, he must divorce her and pay her ketubah. According to Rabbi Yehoshua, invalid testimony does not render her forbidden, but once the matter has become so ugly that the women gossip about her while they work, he must divorce her and pay her ketubah, since nothing has been proven.