| FREE ABELIAN LATTICE-ORDERED GROUPS (2008) | |||||||||||||||||
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| Abstract. Let n be a positive integer and F Aℓ(n) be the free abelian latticeordered group on n generators. We prove that F Aℓ(m) and F Aℓ(n) do not satisfy the same first-order sentences in the language L={+, −, 0, ∧, ∨} if m � = n. We also show that T h(F Aℓ(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. Classification: 03B25; 06F20; 20F60 | |||||||||||||||||
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