P-stable polygons are studied. It is proved that the property of being (P, s)-, (P, a)-, and (P, e)-stable for the class of all polygons over a monoid S is equivalent to S being a group. We describe the structure of (P, s)-, (P, a)-, and (P, e)-stable polygons SA over a countable left zero monoid S and, under the condition that the set A \ SA is indiscernible, over a right zero monoid.
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References
E. A. Palyutin, “E ∗-stable theories,” Algebra and Logic, 42, No. 2, 112-120 (2003).
E. A. Palyutin, “P-stable Abelian groups,” Algebra and Logic, 52, No. 5, 404-421 (2013).
M. A. Rusaleev, “Characterization of (p, 1)-stable theories,” Algebra and Logic, 46, No. 3, 188-194 (2007).
D. O. Ptakhov, “Polygons with a P-stable theory,” to appear in Algebra and Logic.
Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], 6th edn., Fizmatlit, Moscow (2011).
C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973).
M. Kilp, U. Knauer, and A. V. Mikhalev, Monoids, Acts and Categories. With Applications to Wreath Products and Graphs. A Handbook for Students and Researchers, de Gruyter Expo. Math., 29, Walter de Gruyter, Berlin (2000).
A. Yu. Avdeyev and I. B. Kozhukhov, “Acts over completely 0-simple semigroups,” Acta Cyb., 14, No. 4, 523-531 (2000).
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Translated from Algebra i Logika, Vol. 56, No. 4, pp. 486-505, July-August, 2017.
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Stepanova, A.A., Ptakhov, D.O. P-Stable Polygons. Algebra Logic 56, 324–336 (2017). https://doi.org/10.1007/s10469-017-9453-6
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DOI: https://doi.org/10.1007/s10469-017-9453-6