Geodesic
Elementary Theory for $l$-Ideal Lattices of Abelian $l$-Groups
Algebra i logika, Tome 44 (2005) no. 5, pp. 540-559.

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A description is furnished for ideal lattices of free vector lattices $\mathcal F_n$ with a finite number $n$ of free generators. It is proved that an elementary theory for $l$-ideal lattices of Abelian lattice-ordered groups is undecidable, which gives a negative solution to Problem 5.20 in the “Kourovka Notebook.”
Keywords: free vector lattice, ideal lattice, elementary theory. 
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N. Ya. Medvedev. Elementary Theory for $l$-Ideal Lattices of Abelian $l$-Groups. Algebra i logika, Tome 44 (2005) no. 5, pp. 540-559. http://geodesic.mathdoc.fr/item/AL_2005_44_5_a1/

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