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Large rigid sets of algebras with respect to embeddability

  • Gábor Czédli EMAIL logo and Danica Jakubíková-Studenovská EMAIL logo
Published/Copyright: July 5, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 2

Abstract

Let τ be a nonempty similarity type of algebras. A set H of τ-algebras is called rigid with respect to embeddability, if whenever A, B ∈ H and φ: A → B is an embedding, then A = B and φ is the identity map. We prove that if τ is a nonempty similarity type and 𝖒 is a cardinal such that no inaccessible cardinal is smaller than or equal to m, then there exists a set H of τ-algebras such that H is rigid with respect to embeddability and |H| = 𝖒. This result strengthens a result proved by the second author in 1980.

Key words: embedding; antichain; inaccessible cardinal; rigid algebra; discrete category of algebras; monounary algebra
MSC 2010: Primary 08A35; Secondary 08A60; 08C99

Dedicated to Anatolij Dvurečenskij on his 65th birthday

(Communicated by Sylvia Pulmannová)

This research of the first author was supported by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A-11/1/KONV-2012-0073”, and by NFSR of Hungary (OTKA), grant number K83219. The work of the second author was supported by VEGA Grant No. 1/0063/14.

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Received: 2014-2-12
Accepted: 2014-10-24
Published Online: 2016-7-5
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0145
Keywords for this article
embedding; antichain; inaccessible cardinal; rigid algebra; discrete category of algebras; monounary algebra

Articles in the same Issue

  1. Research Article
  2. Holistic logical arguments in quantum computation
  3. Research Article
  4. States with values in the Łukasiewicz groupoid
  5. Research Article
  6. On realization of effect algebras
  7. Research Article
  8. States on symmetric logics: extensions
  9. Research Article
  10. Extensions and measurability in quantum measure spaces
  11. Research Article
  12. Convex subalgebras of upper bounded GMV-algebras
  13. Research Article
  14. Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra
  15. Research Article
  16. Large rigid sets of algebras with respect to embeddability
  17. Research Article
  18. Conformal algebras, vertex algebras, and the logic of locality
  19. Research Article
  20. Extension of measures on pseudo-D-lattices
  21. Research Article
  22. Note on a parameter switching method for nonlinear ODEs
  23. Research Article
  24. Compatibility for probabilistic theories
  25. Research Article
  26. Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras
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  28. Commutativity in a synaptic algebra
  29. Research Article
  30. Discrete averaged mixing applied to the logarithmic distributions
  31. Research Article
  32. Automorphisms of decompositions
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