Skip to main content

Three Lectures on the RS Problem

  • Chapter
Algebraic Model Theory

Part of the book series: NATO ASI Series ((ASIC,volume 496))

Abstract

In these lectures we return to the RS Problem discussed in E. Kiss’s article (this volume). We discuss the current status of the problem and describe some results which arose from the study of the problem, including the solution to Tarski’s finite basis problem. A subtitle for these lectures might be “Some recent results in general algebra, mostly due to R. McKenzie.”

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Baker, G. McNulty and H. Werner, Shift-automorphism methods for inherently nonunitely based varieties of algebras, Czechoslovak Math. J. 39 (1989), 53–69.

    MathSciNet  Google Scholar 

  2. S. Burris and H. Werner, Sheaf constructions and their elementary properties, Trans. Amer. Math. Soc. 248 (1979), 269–309.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Freese and R. McKenzie, Commutator Theory for Congruence Modular Varieties, London Mathematical Society Lecture Note Series, 125, Cambridge University Press, Cambridge-New York, 1987.

    MATH  Google Scholar 

  4. D. Hobby, Finding type sets is NP-hard. Internat. J. Algebra Comput. 1 (1991), 437–444.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics, 76, American Mathematical Society, Providence,RI, 1988.

    Book  Google Scholar 

  6. K. Kearnes, E. Kiss and M. Valeriote, Minimal sets and varieties, Trans. Amer. Math. Soc., to appear.

    Google Scholar 

  7. K. Kearnes, E. Kiss and M. Valeriote, A geometric consequence of residual smallness, manuscript, 1996.

    Google Scholar 

  8. R. McKenzie, The residual bounds of unite algebras, Internat. J. Algebra Comput. 6 (1996), 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. McKenzie, The residual bound of a finite algebra is not computable, Internat. J. Algebra Comput. 6 (1996), 29–48.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. McKenzie, Tarski’s finite basis problem is undecidable, Internat. J. Algebra Comput. 6 (1996), 49–104.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. McKenzie, The type-set of a variety is not computable, manuscript, 1995.

    Google Scholar 

  12. R. McKenzie, Recursive inseparability for residual bounds of finite algebras, manuscript, 1995.

    Google Scholar 

  13. R. McKenzie, Residual smallness relativized to congruence types, manuscript, 1996.

    Google Scholar 

  14. G. McNulty, Residual flniteness and finite equational bases: undecidable properties of finite algebras, manuscript, 1996.

    Google Scholar 

  15. A. Szendrei, Maximal non-affine reducts of simple affine algebras, Algebra Universalis 34 (1995), 144–174.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Szendrei, Strongly abelian minimal varieties, Acta Sci. Math. (Szeged) 59 (1994), 25–42.

    MathSciNet  MATH  Google Scholar 

  17. R. Willard, Tarski’s finite basis problem via A(T), Trans. Amer. Math. Soc., to appear.

    Google Scholar 

  18. R. Willard, Determining whether HSP(A) has a model companion is undecidable, manuscript, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Willard, R. (1997). Three Lectures on the RS Problem. In: Hart, B.T., Lachlan, A.H., Valeriote, M.A. (eds) Algebraic Model Theory. NATO ASI Series, vol 496. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8923-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8923-9_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4884-4

  • Online ISBN: 978-94-015-8923-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics