On non-archimedean frames
arXiv:2311.18095
Abstract
In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that constitutes a tree to each non-archimedean frame, and then we observe that every non-archimedean frame is a quotient of the frame of opens of the tree's branch space. Moreover, we give a partial answer to when these frames are canonically isomorphic; this leads to considering some choice principles of the resulting tree.
19 pages, 3 figures, several changes has been made on the introduction, preliminaries, in particular a corection to the statement: all non-archimedean frames are spatial, is incorrect, an example of this is provided with some particular statement about the spatiality of these frames