kinyan 4 amos

The Mishna (B.M. 11a) says that if an injured animal or an object falls into a person’s chatzeir and the person declares “zachsa li chatzeiri”, I wish to acquire the object through my chatzeir, he/she is koneh the object.

Tosfos writes that the declaration of “zachsa li chatzeiri” is unnecessary. One of Tosfos’ proofs is from the takanah (see B.M. 10) that 4 amos surrounding a person are koneh without a declaration. The GR”A (see the note printed on the daf) notes that the Rambam disagrees (see Hil Aveidah 17:11, Hil Zechiya 1:4) and always mentions the declaration of “zachsa li”.

Perhaps the point of debate revolves around how to understand this kinyan of 4 amos. Is the kinyan of 4 amos an extension of the basic idea of kinyan chatzeir or a completely new takanah? From the fact that Tosfos lumps the two together, it seems 4 amos and chatzeir share the same basic dynamic. The Rambam, however, perhaps views kinyan 4 amos as a categorically new type of kinyan.