Geodesic
Polygons with a (P, 1)-stable theory
Algebra i logika, Tome 56 (2017) no. 6, pp. 712-720.

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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.
Keywords: $(P,1)$-stable theories
Mots-clés : polygons, $(P,1)$-stable polygons. 
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     title = {Polygons with a {(P,} 1)-stable theory},
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     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_6_a4/}
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D. O. Ptakhov. Polygons with a (P, 1)-stable theory. Algebra i logika, Tome 56 (2017) no. 6, pp. 712-720. http://geodesic.mathdoc.fr/item/AL_2017_56_6_a4/

[1] E. A. Palyutin, “$E^*$-stabilnye teorii”, Algebra i logika, 42:2 (2003), 194–210 | MR | Zbl

[2] M. A. Rusaleev, “Kharakterizatsiya $(p,1)$-stabilnykh teorii”, Algebra i logika, 46:3 (2007), 346–359 | MR | Zbl

[3] Yu. L. Ershov, E. A. Palyutin, Matematicheskaya logika, 6-e izd., Fizmatlit, M., 2011 | MR

[4] G. Keisler, Ch. Chen, Teoriya modelei, Mir, M., 1977 | MR

[5] M. Kilp, U. Knauer, 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 | MR

[6] A. Yu. Avdeyev, I. B. Kozhukhov, “Acts over completely 0-simple semigroups”, Acta Cybern., 14:4 (2000), 523–531 | MR