Abstract
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.
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References
A. A. Stepanova, “Primitive connected and additive theories of polygons,” Algebra Logika, 45, No. 3, 300–313 (2006).
E. A. Palyutin, “Primitive connected theories,” Algebra Logika, 39, No. 2, 145–169 (2000).
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Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-2810.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 4, pp. 491–508, July–August, 2008.
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Stepanova, A.A. Polygons with primitive normal and additive theories. Algebra Logic 47, 279–288 (2008). https://doi.org/10.1007/s10469-008-9019-8
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DOI: https://doi.org/10.1007/s10469-008-9019-8