On the relative strength of the representation theorems for \(l\)-groups

DOI10.1007/BF01182094zbMath0869.06012OpenAlexW2042711970MaRDI QIDQ1905985

Daniel Gluschankof

Publication date: 2 September 1997

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

Full work available at URL: https://doi.org/10.1007/bf01182094

zbMATH Keywords

representation theoremsZermelo-Fraenkel set theoryBoolean Prime Ideal Theoremrelative strengthclasses of \(\ell\)-groupssubdirect product of subdirectly irreducible algebras

Mathematics Subject Classification ID

Ordered groups (06F15) Subdirect products and subdirect irreducibility (08B26) Axiom of choice and related propositions (03E25)

Cites Work

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• Birkhoff's representation theorem is equivalent to the axiom of choice
• The lattice-ordered group of automorphisms of an ordered set
• Hyper-regular lattice-ordered groups
• The Hahn Embedding Theorem for Abelian Lattice-Ordered Groups
• The axiom of choice

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