The Archimedean property: new horizons and perspectives

DOI10.1007/s00012-018-0573-1OpenAlexW2900675801WikidataQ128815623 ScholiaQ128815623MaRDI QIDQ1630814

Antonio Ledda, Francesco Paoli, Constantine Tsinakis

Publication date: 5 December 2018

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00012-018-0573-1

zbMATH Keywords

lattice-ordered groupsubstructural logicresiduated latticeArchimedean propertygeneralized MV-algebrageneralized BL-algebraConrad's program

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) MV-algebras (06D35) Ordered semigroups and monoids (06F05) Ordered groups (06F15) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47)

Related Items (1)

Nilpotency and the Hamiltonian property for cancellative residuated lattices

Uses Software

• Pseudo Hoops

Cites Work

• Projectable \(\ell\)-groups and algebras of logic: categorical and algebraic connections.
• Varieties generated by unital abelian \(\ell\)-groups
• Multipotent GBL-algebras
• Archimedean lattices
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• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Substructural logics: a primer
• Generalized MV-algebras
• Products of classes of residuated structures
• Varieties of BL-algebras. I: General properties.
• Algebraic foundations of many-valued reasoning
• Hulls of ordered algebras: projectability, strong projectability and lateral completeness
• Lattice-theoretic properties of algebras of logic
• Cancellative residuated lattices
• THE STRUCTURE OF RESIDUATED LATTICES
• Some Structure Theorems for Lattice-Ordered Groups
• Hyper-Archimedean BL-algebras are MV-algebras
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• The Largest Proper Variety of Lattice Ordered Groups
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• Non-Commutative Residuated Lattices
• On pseudo MV-algebras
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