Free abelian lattice-ordered groups

Annals of Pure and Applied Logic 134 (2-3):265-283 (2005)

Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices
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DOI 10.1016/j.apal.2004.10.017
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Undecidability of Some Topological Theories.Andrzej Grzegorczyk - 1953 - Journal of Symbolic Logic 18 (1):73-74.
Elementary Properties of Abelian Groups.W. Szmielew - 1959 - Journal of Symbolic Logic 24 (1):59-59.

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