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The essentially free spectrum of a variety

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Abstract

We partially prove a conjecture from [MeSh] which says that the spectrum of almost free, essentially free non-free algebras in a variety is either empty or consists of the class of all successor cardinals.

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References

  • [EkMe] P. C. Eklof and A. H. Mekler,Almost Free Modules: Set-theoretic Methods, North-Holland, Amsterdam, 1990.

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  • [MeSh] A. H. Mekler and S. Shelah,Almost free algebras, Israel Journal of Mathematics89 (1995), 237–259.

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  • [Sh] S. Shelah,A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel Journal of Mathematics21 (1975), 319–349.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Alan H. Mekler

  2. Institute of Mathematics, The Hebrew University of Jerusalrm, Givat Ram, 91904, Jerusalem, Israel

    Saharon Shelah

  3. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Otmar Spinas

Authors
  1. Alan H. Mekler
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  2. Saharon Shelah
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  3. Otmar Spinas
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Additional information

The author was supported by the NSERC. Prof. Mekler died on June 10, 1992.

The author is supported by the United States-Israel Binational Science Foundation; publication 417.

The author is supported by the Schweizer Nationalfonds.

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Mekler, A.H., Shelah, S. & Spinas, O. The essentially free spectrum of a variety. Israel J. Math. 93, 1–8 (1996). https://doi.org/10.1007/BF02761091

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  • DOI: https://doi.org/10.1007/BF02761091

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