Rav Dimi of Neharde’a taught that when someone sells a house to another person, even if the terms umka ve-ruma – to the depths and heights – are included in the contract, it must specify mi-tehom ara ve-ad rum rekia – from the depths of the earth until the heights of the sky. The Gemara explains that the mere mention of depths and heights is not specific enough to clarify that further rights are included in the sale, beyond the house itself.
Based on this ruling, if the rights to the air and ground were not included in the contract, the purchaser would not be allowed to dig under the house, nor build above it; those rights were retained by the seller. In fact, the purchaser may be able to keep the seller from actually building above or below the house if such a project would threaten the stability of the existing structure that he bought. The Ri Migash rules that the seller does not really have the right to perform such construction, but if the purchaser dug underground, for example, it would belong to the seller.
The rishonim comment that this is true only in a situation where a house is being sold. If a field was being sold, however, it is clear that the sale includes more than just the surface of the land itself. According to the Re’ah and Ritva, both air rights and rights to what lies beneath the ground must be included, since a field is worthless if the owner cannot make use of those rights – the air rights for sun, rain and wind, and the ground for underground moisture. The Rashba argues that this is true for air rights, but rights to the ground must be specified.