The Mishnah (15:1) teaches that a thick woolen garment (segos) or thick block of wood (kofet) that is on the floor, does not act as an ohel unless it is raised a tephach above the ground. In other words, if there was tumat hamet and a kli underneath the block, the kli would remain tahor. The Bartenura explains that the principle behind this Mishnah has been taught previously where the Mishnah (11:3) discussed a case of porch that has a crack along its width, dividing it into two ohalot. The Mishnah addresses whether the segos or kofet that is reseting beneath that crack can act as an ohel to spread the tumah from one side to the other and provides the same criteria. In other words, despite the segos and kofet being thicker than a tephach, we do not subtract the space below the tephach and define the top as an ohel.
The Tosfot Yom Tov cites the Maharam that explains that this Mishnah is still necessary. One might have thought that the reason why the segos that rests on the floor could not act as an ohel to spread tumah from one side of the crack to the other is because we need two principles to make it work. The first is to view the thickness up to a tephach is if it were not there. The second is to apply the principle of gud asik to the thickness above the tephach, that we consider the edge as if it extends to the ceiling, such that it seals the crack. One might think that the reason that the segos is ineffective is because it is too much to apply both principles. However, in our case, where only one is required, one might have thought that the segos could act as an ohel. Consequently our Mishnah is necessary to explain that even in this case, it cannot act as an ohel.
The Mishnah Achrona however cites a question from the Mishnat Chachamim. It would seems that even if the kofet does not act as an ohel to spread the tumah the kli should still be tameh. Recall that an object that comes into contact with a corpse becomes an avi avot ha'tumah -- the same level of tumah as the corpse -- based on the pasuk "be'chalel cherev". The Bartenura explained (11:8) that such an object would transfer tumah be'ohel. In other words, in our case even if the segos is not touching the met or kli, and there is less than a tephach between them, the segos would become an avi avot ha'tumah and make everything beneath it, including the kli, tameh.
The Mishnat Chachamim suggests that perhaps the Bartenura takes the position of Rabbeinu Tam that cherev ke'chalel -- that a vessel that comes into contact with a corpse is also an avi avot ha'tumah -- only applies to metal keilim (see Volume 18 Issue 19). Consequently, since neither of the objects in our Mishnah are metal, they would only become an av ha'tumah, and if they did not touch the kli, it would remain tahor.
The Mishnah Achrona suggests that we can even understand the Mishnah according to the Bartenura and maintain cherev ke'chalel applies to other materials. While the segos would become an avi avot ha'tumah, the reason why the kli remains tahor is that since the segos is not a tephach above the kli it is not considered as if it is acting as an ohel, i.e. covering over the kli.
The issue with this suggestion is that the Bartenura maintains that if the space is less than a tephach it is considered as if they are in direct contact. Recall that we learnt (3:1) that if one is touching a half kezayit and his hand is over the top of another half ketzayit the two combine to make the person tameh. The Baterenura explains this is when there is less than a tephach between his hand and the tumah. When there is less than a tephach the tumah spreads upwards -- boke'ah ve'oleh - making everything tameh. Consequently, it is considered as if he is touching the tumah and therefore it is considered as if he is in direct contact with a full kezayit. Consequently, in our case, it should be considered as if the segos that is tameh is in direct contact with the kli and it should therefore be tameh. The Mishnah Achrona however answers that the law that if it is less than a tephach it is considered as if it is in direct contact is only with respect to the tumat met; since it would be bokeh ve'olah, it is viewed as if it is in direct contact. With respect to the segos and the kli after that however, this would not be the case -- a gap of less than a tephach is not considered as if it is in direct contact.1
1 The Mishnah Achrona's conclusion would then appear to support the Mishnat Chachamim since if the segos would be considered an avi avot ha'tumah, since it is metameh be'ohel, it would make the kli tameh even when the gap is less than a tephach, [וצ״ע]{dir="rtl"}.
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