Local-global properties of positive primitive formulas in the theory of spaces of orderings

At the same time, spaces of orderings occur naturally in a wide variety of contexts: semilocal rings [13] (more generally, rings with many units [22]) or skewfields [9] (more generally, domains [15] or ternary fields [12]) or ∗–fields with involution [10] (more generally, ∗–domains [19]). Spaces of orderings are the ‘local objects’ in the ‘global’ theory of spaces of signs (abstract real spectra) developed in [1] [18].