Geodesic
Near Regularly-Pr\"ufer Rings
Matematičeskie trudy, Tome 2 (1999) no. 1, pp. 72-120.

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In the present article, we construct the theory of near Boolean families of valuation rings which extends the corresponding theory for Boolean families. We establish the fact that the local-global principle (LGP) for such families is effectively elementary. We indicate sufficient conditions for 1-embeddability of holomorphy rings of near Boolean families that possess the LGP property. By way of application, we prove that the elementary theory of the ring of integrably totally $p$-adic integers and the elementary theory of the class of all closed subrings of almost all algebraic numbers are decidable. 
@article{MT_1999_2_1_a2,
     author = {Yu. L. Ershov},
     title = {Near {Regularly-Pr\"ufer} {Rings}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {72--120},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_1999_2_1_a2/}
}
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Yu. L. Ershov. Near Regularly-Pr\"ufer Rings. Matematičeskie trudy, Tome 2 (1999) no. 1, pp. 72-120. http://geodesic.mathdoc.fr/item/MT_1999_2_1_a2/