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

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References

  1. H. Andréka andI. Németi,HSPK is an equational class, without the Axiom of Choice. Algebra Universalis,13 (1981), 164–166.

    Google Scholar 

  2. H. Andréka andI. Németi,Does SPK⊃-PSK imply the Axiom of Choice? Comment. Math Univ. Carolina,21 (1980), 699–706.

    Google Scholar 

  3. H.Andréka, D.Monk, and I.Németi,The Axiom of Foundation and operators on classes of algebra, Manuscript.

  4. G. Grätzer,Universal Algebra, Second Edition. Springer Verlag, New York, Heidelberg, Berlin, 1979.

    Google Scholar 

  5. G. Grätzer,A statement equivalent to the Axiom of Choice. Abstract: Notices Amer. Math. Soc.12 (1965), 217.

    Google Scholar 

  6. K. Kunen,Set Theory, An Introduction to Independence Proofs. Studies in Logic and the Foundations of Mathematics. North Holland Publishing Company, Amsterdam, 1980.

    Google Scholar 

  7. H. Rubin andJ. Rubin,Equivalents of the Axiom of Choice. Studies in Logic and the Foundations of Mathematics. North Holland Publishing Company, Amsterdam, 1963.

    Google Scholar 

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To the memory of András Huhn

Research supported by NSERC of Canada.

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Grätzer, G. Birkhoff's representation theorem is equivalent to the axiom of choice. Algebra Universalis 23, 58–60 (1986). https://doi.org/10.1007/BF01190911

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  • DOI: https://doi.org/10.1007/BF01190911

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