Free abelian lattice-ordered groups

Abstract. Let n be a positive integer and FA (n) be the free abelian latticeordered group on n generators. We prove that FA (m) and FA (n) do not satisfy the same first-order sentences in the language L={+, -, 0, , } if m = n. We also show that Th(FA (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

• Type: Journal
• Year: 2005
• Where: APAL
• Authors: Andrew M. W. Glass, Angus Macintyre, Françoise Point
• Keywords: Abelian Latticeordered Group, APAL 2005, First-order Sentences, Positive Integer