Kiddushin, Chapter Three, Mishnah Thirteen
This mishnah continues to discuss personal status and lineage. The specific issue is whether or not a mamzer can purify his lineage.
Rabbi Tarfon says: mamzerim can be purified.
How is this so? If a mamzer marries a slave woman, her son is a slave; if he frees him, it is found that the son is a free man.
Rabbi Eliezer says: behold, he is a slave mamzer.
Rabbi Tarfon uses the rules in the previous mishnah to find a means by which a mamzer can have a child that is not a mamzer. A mamzer is allowed to marry a slave woman, even though a non-mamzer cannot. If the mamzer owns the slave woman, then he owns the child. If he frees the child the child loses his mamzer status and becomes a regular Israelite.
Rabbi Eliezer, however, holds that such a trick does not work. The status of the child is slave mamzer. When his father/master frees him, he is no longer a slave but he is still a mamzer.