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. 
@article{FPM_2008_14_7_a3,
     author = {E. I. Bunina and A. S. Dobrokhotova-Maykova},
     title = {Elementary equivalence of generalized incidence rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {37--42},
     publisher = {mathdoc},
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     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a3/}
}
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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/