Abstract
We give necessary and sufficient conditions for the first-order theory of a finitely presented abelian lattice-ordered group to be decidable. We also show that if the number of generators is at most 3, then elementary equivalence implies isomorphism. We deduce from our methods that the theory of the free MV-algebra on at least 2 generators is undecidable.
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Glass, A.M.W., Point, F. (2007). Finitely Presented Abelian Lattice-Ordered Groups. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_11
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DOI: https://doi.org/10.1007/978-3-540-75939-3_11
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