Existentially complete abelian lattice-ordered groups
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Existentially Complete Abelian Lattice-ordered Groups
The theory of abelian totally ordered groups has a model completion. We show that the theory of abelian lattice-ordered groups has no model companion. Indeed, the Archimedean property can be captured by a first order V3V sentence for existentially complete abelian lattice-ordered
On the Congruence Lattice of an Abelian Lattice Ordered Group
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
Finitely Presented Abelian Lattice-Ordered Groups
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 th
Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one
It is well known that the lattice $${{\,\mathrm{Id_c}\,}}{G}$$ of all principal $$\ell $$ -ideals any Abelian -group G a completely normal distributive 0-lattice; yet not every 0-lattice homomorphic image some , via counterexample cardinality $$\aleph _2$$ . We prove with at most
Free abelian lattice-ordered groups
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 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Final
On cut completions of abelian lattice ordered groups