to forbidden sex for which one is liable for violation of a prohibition concerning which a betrothal between the couple would take effect. However, here, with regard to a non-Jew and a slave, since their betrothal of a Jewish woman would not take effect, a union with them is comparable to forbidden sex for which one is liable to receive karet, and therefore the offspring of such a union will be a mamzer.
מיתיבי: גוי ועבד הבא על בת ישראל — הולד ממזר. רבי שמעון בן יהודה אומר: אין ממזר אלא ממי שאיסורו איסור ערוה וענוש כרת.
The Talmud raises an objection from a baraita: In the case of a non-Jew or a slave who had sex with a Jewish woman, the offspring born from such a union is a mamzer. R' Shimon ben Yehuda says: The offspring is a mamzer only if born from sex with one who is forbidden by a prohibition of forbidden sex that are punishable by karet. It is apparent from the baraita that one who holds, as does Shimon HaTimni, that only the offspring from forbidden sex for which one is liable to receive karet is a mamzer, nevertheless holds that the offspring of a slave or non-Jew and a Jewish woman is not a mamzer.
אלא אמר רב יוסף: מאן ״הכל מודים״ — רבי, אף על גב דרבי אומר: אין הדברים הללו אמורים אלא לדברי רבי עקיבא, שהיה עושה חלוצה כערוה, וליה לא סבירא ליה, בגוי ועבד מודה. דכי אתא רב דימי, אמר רב יצחק בר אבודימי משום רבינו: גוי ועבד הבא על בת ישראל — הולד ממזר.
Rather, Rav Yosef said: Who is included by saying: All agree? It is R' Yehuda HaNasi, as although R' Yehuda HaNasi says in a baraita (52b) concerning the Mishnah (50a–51b) that states that a levirate betrothal between a yavam and a yevama with whom he had already performed ḥalitza is ineffective: This statement was said only according to the statement of R' Akiva, as he would consider a ḥalutza like a forbidden relative such that if the yavam betrothed her it would not take effect. And although R' Yehuda HaNasi himself does not hold accordingly with regard to that issue, with regard to the offspring of a union with a non-Jew or a slave he concedes that the offspring is a mamzer. As, when Rav Dimi came from Eretz Yisrael, he said that Rav Yitzḥak bar Avudimi said in the name of our Master, i.e., R' Yehuda HaNasi: With regard to a non-Jew or a slave who had sex with a Jewish woman, the offspring is a mamzer.