Polygons with primitive normal and additive theories

摘要

Previously, primitive normal, primitive connected, and additive theories of S-polygons were studied. In particular, it was proved that the class of all S-polygons is primitive normal iff S is a linearly ordered monoid. The present paper is a continuation of this research. Here, Spolygons with primitive normal, additive, and antiadditive theories are described in the language of a primitive equivalence structure. It is shown that the class of all S-polygons is antiadditive only for a linearly ordered monoid S, that is, this class is antiadditive iff it is primitive normal.