Geodesic
Elementary equivalence of generalized incidence rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 37-42
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In this paper, we prove that if two generalized incidence rings $I(P_1,R_1)$ and $I(P_2,R_2)$ are elementarily equivalent, then the corresponding ordered sets $(P_1,R_1)$ and $(P_2,R_2)$ are elementarily equivalent. 
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E. I. Bunina; A. S. Dobrokhotova-Maykova. Elementary equivalence of generalized incidence rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 37-42. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a3/

[1] Maltsev A. I., “Ob elementarnykh svoistvakh lineinykh grupp”, Problemy matematiki i mekhaniki, Novosibirsk, 1961, 110–132 | Zbl

[2] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990 | MR

[3] Shmatkov V. D., Izomorfizmy i avtomorfizmy kolets i algebr intsidentnosti, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1994

[4] Belding W., “Incidence rings of pre-ordered sets”, Notre Dame J. Formal Logic, 14 (1973), 481–509 | DOI | MR | Zbl

[5] Doubilet P., Rota G.-C., Stanley R. P., “On the foundation of combinatorial theory. VI. The idea of generating functions”, Proc. of the Sixth Berkeley Symp. on Math. Stat. and Probab., Vol. 2, Univ. California Press, 1972, 267–318 ; Perechislitelnye zadachi kombinatornogo analiza, eds. G. P. Gavrilov, Mir, M., 1979, 160–228 | MR | Zbl | MR

[6] Finch P. D., “On the Möbius-function of non singular binary relation”, Bull. Austral. Math. Soc., 3 (1970), 155–162 | DOI | MR | Zbl

[7] Rota G.-C., “On the foundation of combinatorial theory. I. Theory of Möbius functions”, Z. Wahrsch. Verw. Gebiete, 2:4 (1964), 340–368 | DOI | MR | Zbl

[8] Stanley R. P., “Structure of incidence algebras and their automorphism groups”, Amer. Math. Soc. Bull., 76 (1970), 1236–1239 | DOI | MR | Zbl

[9] Tainiter M., “Incidence algebras on generalized semigroups”, J. Combin. Theory, 11 (1971), 170–177 | DOI | MR | Zbl