Forcing of Infinity and Algebras of Distributions of Binary Semi-isolating Formulas for Strongly Minimal Theories

摘要

We apply a general approach for distributions of binary isolating and semi-isolating formulas to the class of strongly minimal theories. For this aim we introduce and use the notion of forcing of infinity. Structures associated with binary formulas, in strongly minimal theories, and containing compositions and Boolean combinations are characterized: a list of basic structural properties for these structures, including the forcing of infinity, is presented, and it is shown that structures satisfying this list of properties are realized in strongly minimal theories.