ViraScience.
Open-access article

Existentially complete abelian lattice-ordered groups

A. M. W.Glass, Keith R.Pierce

Abstract

No abstract recorded for this item.

Similar items

  • Existentially Complete Abelian Lattice-ordered Groups

    Scholarly record2010KEITH R. PIERCE, K. R. PIERCE

    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

    Scholarly record2002Ján Jakubík

    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

    Scholarly record2006Algebraic and Proof-theoretic Aspects of Non-classical LogicsAndrew M. W. Glass, Françoise Point

    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

    Open-access article2023Acta Scientiarum Mathematicarum['Miroslav Ploščica', 'Friedrich Wehrung', '']

    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

    Scholarly record2005Ann. Pure Appl. LogicAndrew M. W. Glass, Angus Macintyre, Françoise Point

    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

    Open-access article2000Czechoslovak Mathematical JournalJánJakubík