Geodesic
The hereditarily undecidability of one class of lattice-ordered Abelian groups
Algebra i logika, Tome 6 (1967) no. 1, pp. 45-62.

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Let $G$ be an Abelian $\ell$-group. We denote through $G$ the lattice of all $\hat g$ with $g\in G$ (see [2]). Let $L$ be the class of all such Abelian $\ell$-group $G$ so that $G$ is divisible and Archimedean and $\hat G$ is atomic Boolean algebra. \underline{THEOREM 1.} (Elementary) theory of $L$ is hereditarily undecidable. 
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     author = {Yu. \v{S}. Gurevich},
     title = {The hereditarily undecidability of one class of lattice-ordered {Abelian} groups},
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     pages = {45--62},
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     volume = {6},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_1967_6_1_a5/}
}
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Yu. Š. Gurevich. The hereditarily undecidability of one class of lattice-ordered Abelian groups. Algebra i logika, Tome 6 (1967) no. 1, pp. 45-62. http://geodesic.mathdoc.fr/item/AL_1967_6_1_a5/