2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149852This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The methods used are the real spectrum and Zariski's theory of complete ideals.12 pages, TeX version 3.1Algebraic GeometryComplete ideals defined by sign conditions and the real spectrum of a two-dimensional local ringtext