What is Kares?

At the end of his commentary to the first of this week's double-portion, the Ramban has a long discussion of what the punishment of kares, generally translated as excision, means. "For whoever does any of these abominations, even the souls who do them will be cut off from among their people" (Lev. 18:29). To move this discussion further by a few centuries, I will summarize, reformulate and add a little to the discussion of this topic by Abarbanel, in his commentary to Numbers 15:22. Abarbanel discusses seven different views of the subject:

1. R. Sa'adia Gaon, says Abarbanel, holds that the soul that is cut off is the physical body. Kares means dying before your time. I assume that Abarbanel's source is Emunos Ve-Dei'os and not R. Sa'adia Gaon's Arabic translation of the Torah. If it is the latter, I could not find anything relevant in R. Yosef Kafach's retranslation back into Hebrew, but I could have missed it. Regardless, I don't think Abarbanel read Arabic (see Netanyahu's Don Isaac Abravanel, p. 268 n. 33). In Emunos Ve-Dei'os (9:9), R. Sa'adia Gaon writes (my translation from R. Yosef Kafach's Hebrew, p. 282): "His excision from this world causes him to be excised from among the righteous also in the world-to-come because he did not repent. And if God did not excise him, but completed his days in His patience, and he still did not repent, his punishment is even greater and his excision from among the righteous is even more deserved." It seems to me that R. Sa'adia Gaon believed that kares means that generally, absent Divine mercy, a person will die before his time and, if he fails to repent, will be punished in the afterlife by being removed from righteous souls. I'm not sure how Abarbanel read this passage.
   
2. Rashi held that kares means dying young and losing, or failing to have, progeny. Rashi writes this in his commentary to the Torah (Lev. 17:9) and in a few places in his commentary to the Talmud (Shabbos 25a sv. ve-kares; Chullin 31a sv. tamei; Kerisus 2a sv. Pesach; Kesubos 30b sv. zar; Ta'anis 5b ve-ha'amar) and is discussed by Tosafos (Yevamos 2a sv. eishes; Shabbos 25a sv. kares). Actually, Rashi sometimes says that kares means that you die young, sometimes that you have no progeny and sometimes both. The simple resolution is that he means both but sometimes only mentions one aspect of it.
3. The Riva, in Tosafos (cited above), believes that kares means you die at the age of 50, or at least before 60. Additionally, and this is unreported by Abarbanel, Riva holds that those who violate the prohibitions of forbidden relations, about whom it is stated "aririm yihyu -- they shall be childless", die without progeny. Also in Tosafos is the qualification of Rabbenu Tam that only children who are minors can be punished for their parents' sins. Dying childless does not apply to children who are adults at the time of their parents' sin.
4. Abarbanel quotes another view from Tosafos that kares means dying after three days of illness. I could not locate this view. Abarbanel quotes a Gemara (Mo'ed Katan 28a) as proof but the Levush, who directs readers to Tosafos across the Talmud that quote a passage, does not indicate any Tosafos that utilizes this Gemara. I'm not sure what text Abarbanel had before him.
5. The Rambam's view has been interpreted in three different ways. In his commentary to Sanhedrin (9:6), Rambam writes that someone who receives kares is punished also in the world-to-come, as he explains in the next chapter. But in the introduction to the next chapter (p. 138 in the Hebrew-only R. Kafach edition), he writes that kares is that the soul is cut off and destroyed in the world-to-come. Which is it? Is the soul punished or destroyed? In Mishneh Torah (Hilkhos Teshuvah 8:5), the Rambam writes that kares means that the soul does not merit the world-to-come. Ramban, in Toras Ha-Adam (Kisvei Ha-Ramban, vol. 2 pp. 291-293), quoted at length in the anonymous commentary published in the standard edition of Hilkhos Teshuvah, explains that according to the Rambam, kares means that a soul is punished harshly immediately after death and then is destroyed. That allows for both punishment in the afterlife and destruction of the soul. Radbaz (Responsa, vol. 5 no. 122 = no. 1,495) agrees with the Ramban. However, Abarbanel interprets the Rambam differently. He explains that the soul's destruction after death is itself a terrible punishment. There is no suffering of the soul per se, just a great loss of the wonders of the world-to-come. R. Yosef Kafach (Mishneh Torah, Hilkhos Teshuvah ch. 8 n. 4) offers a different interpretation. He suggests that the Rambam's view is that kares is an eternal suffering of the soul. See below for further opposition to the idea that the soul is destroyed.
6. The Ramban, in his commentary to Leviticus (18:29) and Toras Ha-Adam (Kisvei Ha-Ramban, vol. 2 pp. 288-290), distinguishes between three types of kares. Someone who is generally good will be punished with a shortened life but no punishment in the afterlife. Someone who is generally bad will be punished only in the afterlife, meaning punishment and then destruction of the soul. And someone who worships idols or curses God will be punished with both a shortened life and punishment (and afterwards destruction) in the afterlife.
7. Abarbanel then offers his own approach. Kares is always punished with death before the time one would otherwise die and suffering in the afterlife. However, the suffering in the afterlife is limited to a prescribed amount of time, depending on the depth of one's sin, after which one receives the good of the afterlife. This idea that kares in the afterlife does not mean its destruction seems to be the view of two students of Ramban: Rabbenu Bachya ben Asher (commentary to Gen. 25:9, but contrast with his commentary to Lev. 18:29) and Rabbenu David Bonfil (commentary to Sanhedrin 90b, cited in Margoliyos Ha-Yam 90b:14).