A corpse can transfer tumah through an ohel in three ways:
The first two types of tumat ohel seemingly work in a different way to the third. The Mishnah (3:1) states that two half kzeitim of a corpse can combine to transfer tumah as long as they are both transferring tumah in the same way (i.e. both through contact, through carrying or through ohel). According to Chachamim, if someone touches a half kzayit and is maahil over a half kzayit or a half kzayit is maahil over him, he becomes tameh. On the other hand, if someone touches a half kzayit and is present in an ohel with another half kzayit then he does not become tameh, since the first half kzayit is transferring tumah through tumat maga, whereas the second through tumat ohel. This Mishnah implies that the first two types transfer tumah due to the principle of “tumah bokaat v'olah, bokaat v'yoredet” (the tumah extends upwards and downwards). Therefore, when a person places himself directly above or below the tumah, it is as if he is in contact with the tumah - similar to tumat maga (see Gemara Chullin 125b and Rashi there). That is why it combines with tumat maga. On the other hand, if a person is present in an ohel with tumah, that is a separate category and cannot combine with tumat maga.
Conceptually, the third type of tumat ohel may also be different to the first two in its transfer of tumah. In the first two, the person becomes tameh because of an act of 'ahilah' over the corpse (maaseh ahilah). The third type of tumat ohel could be understood to work in two different ways:
The Mishnah (3:7) brings a dispute between R' Yehudah and Chachamim about whether an ohel has to be manmade in order for it to transfer tumah. Chachamim hold that even if an ohel is formed through natural means, it can still transfer tumah and intercept tumah. R' Yehudah however disagrees (unless the ohel is large – see Rambam Peirush Hamishnah). R' Yehudah seems to make two assumptions:
Chachamim, who disagree with R' Yehudah could reject either assumption. Either they hold that tumat ohel does not transfer tumah through it being a 'makom hamet' but through the person performing an act of 'ahilah'. Alternatively, they could agree that tumat ohel transfers though it being 'makom hamet', only that they hold that it can be created even through an ohel that is not manmade.
There are a few practical differences between whether the third type of tumat ohel transfers tumah because of 'ahilah' or it being 'makom hamet'. One is the size that is required to produce an ohel. The Rambam (Tumat Met 12:1) rules (based on 3:7) that any ohel which is a tefach in length, width and height is able to transfer tumah. The Raavad interjects that this only applies when there is a cubed tefach of space aside from the space the tumah occupies. The fact that the Rambam does not mention this implies that he disagrees and the space that the tumah occupies is included in the cubed tefach of space required to form an ohel. The Rambam and Raavad could be disputing the nature of tumat ohel. The Raavad understands that an ohel transfers tumah because of 'ahilah' and therefore a complete tefach of space is required, like any other measurement required in halachah. The Rambam on the other hand, understands that tumat ohel is based on 'makom hamet'. The tumah that is inside the ohel defines the space as 'makom hamet' and therefore, the space that it occupies does not detract from it.
A second difference between these approaches is the required strength of the ohel. The Mishnah (8:2) lists different protrusions and coverings that are not considered an ohel unless they are able to support a layer of cement. One of these mentioned is tree branches. The Rambam (Tumat Met 13:2) rules that any ohel that is not sturdy is not considered an ohel and that tree branches that are not strong enough to hold a layer of cement are not considered an ohel. The Raavad however understands that the Mishnah is not referring to the strength but rather refers to the materials not having significant open spaces. According to the Raavad, if a tree branch does not have significant open spaces, even if it is not sturdy it is still considered an ohel and is able to transfer tumah. The Rambam and Raavad are both consistent with their views. The Rambam is consistent with his view and an ohel that is not sturdy is not sufficient enough to define the space below it as 'makom hamet'. The Raavad on the other hand, holds that even if the ohel is not sturdy, as long as there are no significant open spaces, a person who is present with a corpse under such a material is considered to have performed an act of 'ahilah'.
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