Free abelian lattice-ordered groups
نویسندگان
چکیده
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}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. Classification: 03B25; 06F20; 20F60
منابع مشابه
Sets of Disjoint Elements in Free Products of Lattice-ordered Groups
We show that for every infinite cardinal number m there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality m. This answers problem 10.7 of [13] and extends the results in [12]. We further prove that for the variety of abelian lattice-ordered groups or the variety of all lattice-ordered groups, the fre...
متن کاملExistentially 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 groups, and distinguishes between finitely generic abelian lattice-ordered groups and infinitely generic ones. We th...
متن کاملFinitely 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 that the theory of the free MV -algebra on at least 2 generators is undecidable.
متن کاملInterpreting Formulas of Divisible Lattice Ordered Abelian Groups - Preliminary Version
We show that a large class of divisible abelian `-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the model theory of these `-groups, including decidability results.
متن کاملClassification of Finitely Generated Lattice-ordered Abelian Groups with Order-unit
A unital l-group (G,u) is an abelian group G equipped with a translation-invariant lattice-order and a distinguished element u, called orderunit, whose positive integer multiples eventually dominate each element of G. We classify finitely generated unital l-groups by sequences W = (W0,W1, . . .) of weighted abstract simplicial complexes, where Wt+1 is obtained from Wt either by the classical Al...
متن کاملA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 134 شماره
صفحات -
تاریخ انتشار 2005