Polygons with a (P, 1)-stable theory are considered. A criterion of being (P, 1)-stable for a polygon is established. As a consequence of the main criterion we prove that a polygon SS, where S is a group, is (P, 1)-stable if and only if S is a finite group. It is shown that the class of all polygons with monoid S is (P, 1)-stable only if S is a one-element monoid. (P, 1)-stability criteria are presented for polygons over right and left zero monoids.
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Supported by RFBR, project No. 17-01-00531.
Translated from Algebra i Logika, Vol. 56, No. 6, pp. 712-720, November-December, 2017.
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Ptakhov, D.O. Polygons with a (P, 1)-Stable Theory. Algebra Logic 56, 473–478 (2018). https://doi.org/10.1007/s10469-018-9469-6
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DOI: https://doi.org/10.1007/s10469-018-9469-6