Birkhoff's representation theorem is equivalent to the axiom of choice

DOI10.1007/BF01190911zbMath0615.04009OpenAlexW72257230WikidataQ114694026 ScholiaQ114694026MaRDI QIDQ1820782

George Grätzer

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1007/bf01190911

zbMATH Keywords

axiom of choicesubdirectly irreducible algebrassubdirect productalgebraic lattice\(ZF^ -\)Birkhoff's Representation TheoremCongruence Lattice RepresentationZermelo-Fraenkel set theory without the axiom of foundation

Mathematics Subject Classification ID

Subalgebras, congruence relations (08A30) Axiom of choice and related propositions (03E25)

Related Items (2)

On the relative strength of the representation theorems for \(l\)-groups ⋮ Prime deductive systems and injective objects in the algebras of Łukasiewicz infinite-valued calculi

Cites Work

• Set theory. An introduction to independence proofs
• HSP K is equational class, without the axiom of choice
• Unnamed Item

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