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2 Clarification ; added 12 characters in body
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A mamzer (bastard) is born from an illegal (forbidden) marriage or out of wedlockadultery. However, regarding a gentile, BT (Sot. 26b) states:

דאמר רבי יוחנן משום רבי ישמעאל מנין לעובד כוכבים ועבד שבאו על הכהנת ועל הלוייה ועל בת ישראל שפסלוה שנאמר (ויקרא כב, יג) ובת כהן כי תהיה אלמנה וגרושה מי שיש לו אלמנות וגירושין בה יצאו עובד כוכבים ועבד שאין לו אלמנות וגירושין בה

Rashi concludes (based upon another beraita in San. 52b) that a gentile does not retain matrimonial status.

This said mamzer is prohibited from joining the Jewish nation (SA, EH 4:1). However, we find further on (op cit. 4:21) that a child born from a non-Jewish incestuous relation is not considered a mamzer and is permitted to join the Jewish nation. This would demonstrate that a child born from a relationship which under Jewish law would be considered illegal would not be considered a mamzer because mamzeirus does not apply to illegal unions of gentiles.

A mamzer (bastard) is born from an illegal marriage or out of wedlock. However, regarding a gentile, BT (Sot. 26b) states:

דאמר רבי יוחנן משום רבי ישמעאל מנין לעובד כוכבים ועבד שבאו על הכהנת ועל הלוייה ועל בת ישראל שפסלוה שנאמר (ויקרא כב, יג) ובת כהן כי תהיה אלמנה וגרושה מי שיש לו אלמנות וגירושין בה יצאו עובד כוכבים ועבד שאין לו אלמנות וגירושין בה

Rashi concludes (based upon another beraita in San. 52b) that a gentile does not retain matrimonial status.

This said mamzer is prohibited from joining the Jewish nation (SA, EH 4:1). However, we find further on (op cit. 4:21) that a child born from a non-Jewish incestuous relation is not considered a mamzer and is permitted to join the Jewish nation. This would demonstrate that a child born from a relationship which under Jewish law would be considered illegal would not be considered a mamzer because mamzeirus does not apply to illegal unions of gentiles.

A mamzer (bastard) is born from an illegal (forbidden) marriage or adultery. However, regarding a gentile, BT (Sot. 26b) states:

דאמר רבי יוחנן משום רבי ישמעאל מנין לעובד כוכבים ועבד שבאו על הכהנת ועל הלוייה ועל בת ישראל שפסלוה שנאמר (ויקרא כב, יג) ובת כהן כי תהיה אלמנה וגרושה מי שיש לו אלמנות וגירושין בה יצאו עובד כוכבים ועבד שאין לו אלמנות וגירושין בה

Rashi concludes (based upon another beraita in San. 52b) that a gentile does not retain matrimonial status.

This said mamzer is prohibited from joining the Jewish nation (SA, EH 4:1). However, we find further on (op cit. 4:21) that a child born from a non-Jewish incestuous relation is not considered a mamzer and is permitted to join the Jewish nation. This would demonstrate that a child born from a relationship which under Jewish law would be considered illegal would not be considered a mamzer because mamzeirus does not apply to illegal unions of gentiles.

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A mamzer (bastard) is born from an illegal marriage or out of wedlock. However, regarding a gentile, BT (Sot. 26b) states:

דאמר רבי יוחנן משום רבי ישמעאל מנין לעובד כוכבים ועבד שבאו על הכהנת ועל הלוייה ועל בת ישראל שפסלוה שנאמר (ויקרא כב, יג) ובת כהן כי תהיה אלמנה וגרושה מי שיש לו אלמנות וגירושין בה יצאו עובד כוכבים ועבד שאין לו אלמנות וגירושין בה

Rashi concludes (based upon another beraita in San. 52b) that a gentile does not retain matrimonial status.

This said mamzer is prohibited from joining the Jewish nation (SA, EH 4:1). However, we find further on (op cit. 4:21) that a child born from a non-Jewish incestuous relation is not considered a mamzer and is permitted to join the Jewish nation. This would demonstrate that a child born from a relationship which under Jewish law would be considered illegal would not be considered a mamzer because mamzeirus does not apply to illegal unions of gentiles.