One of the primary messages of masechet Nedarim is how negatively [most of] our Sages viewed the taking of vows. More often than not a vow reflected weakness of character and/or was taken in a moment of anger. The idea that one prohibits another from deriving benefit from oneself (a common type of vow) is playing G-d in the most negative of ways.
The entire approach to nedarim is subtly hinted at in the last sugyah,topic, of the masechet. "In the beginning they would say, three woman are to be divorced from their husbands and receive their ketuba. One who says I am defiled to you..." (Nedarim 90b). Jewish law demands that a man divorce his adulterous wife - even if he be willing to forgive her. While one who admits to having carried out a capital offence cannot be sentenced to death - "a person may not make himself evil" (Sanhedrin 9b) this is a technical law relating to punishment. There is no reason to assume that the person is lying; hence while she would not be given any court-imposed punishment this would be grounds for divorce.
This however was only the original law. Our Sages feared that one could use this law to escape from a marriage. A woman may already have a boyfriend but does not want to commit adultery. By "admitting" that she has done so she could accomplish her goal of leaving one marriage for another. Our Sages thus ordained that she must bring proof that she had an affair. Truth truly is stranger than fiction.
The extent to which our rabbis went to "not believe" evidence of adultery - and thereby forbid a marriage from continuing - can be seen in the concluding piece of the masechet. The Talmud records how an adulterer visited his mistress in her home. Unexpectedly the husband came home and the adulterer quickly hid behind a curtain. He then noticed - unbeknownst to the wife - that the husband was about to eat from some food that had been poisoned by a snake. The adulterer called out to the husband to warn him - effectively turning himself in (and possibly risking his life). Yet the Talmud rules that the wife remains permitted to her husband, arguing that despite appearances no adultery occurred. Had such occurred argue our Sages, the adulterer would have been happy to let the husband eat and die.
Yet even more astonishing than the ruling itself is the Talmudic assertion that the ruling is so obvious it needn't have been stated. Of course no adulterer would try to save the husband, and thus we can be certain adultery did not take place. To this the Talmud - and with this line Maseceht Nedarim comes to a close - argues that maybe it is not so obvious. One might have (incorrectly) argued that yes they committed adultery and the reason the adulterer saved the husband's life is because "stolen waters are sweeter" (Mishlei 9:17). Sin is fun and adultery for many is more "sweet" than a permitted relationship. It is the illicit that sadly gets people excited (just ask any of those exposed by the leak of the Ashley Madison database).
While it is generally true that stolen water are sweeter and an illicit relationship has some extra excitement, as an affair continues the typical adulterer would be much happier if the husband were to "disappear". We can thus be certain that in our particular case no adultery was committed.
 Jewish law allows a woman to demand a divorce from her adulterous husband but does not demand she do so. Perhaps this difference in the law reflected the Talmudic view that being single was much more difficult for a woman than a man. It thus allowed her to continue her relationship with her husband if she so desires but if it was she who committed adultery that option was taken away from her.
For technical reasons the Gemara explains that our case is discussing the wife of a kohen who is raped and is to be divorced from her husband. Nonetheless the general principles involved are relevant for all. In practice the rabbis have made the burden of proof in such a case so high as to almost render this law inapplicable.
Such might get her out of her marriage but would not allow her to marry her lover. Jewish law rules that a woman who has an affair is forbidden to live both with her husband and lover, leba'al vleboel (Sotah 29a). This rabbinic enactment would effectively prevent this woman from marrying another under rabbinic auspices. Of course there is little that can be done to prevent one from disregarding Jewish law.
Even without this psychological argument the husband and wife would remain permitted to each other as lacking two witnesses we have no basis to claim adultery took place. What this argument teaches, notes the Ran, is that even the most pious, who may want to divorce their wife under such circumstances need not, or perhaps should not, do so.
 Our rabbis interpreted the biblical verse "for they have committed adultery, and blood is in their hands" (Yechezkel 23:7) to teach that those who commit adultery are apt to murder the husband and surely would do nothing to save his life. Can there be a better example of the principle how one sin leads to another?