Skip to main content

Polynomially isolated sets

  • Conference paper
  • First Online:
Book cover Recursion Theory Week

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1432))

Supported by NSF grant MCS-83-01850 and by ARO contract DAAG29-85-C-0018.

Supported by NSF grant DMS-85-05004 and by ARO contract DAAG29-85-C-0018.

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight 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.

Bibliography

  1. Crossley, J. N., Aspects of Effective Algebra, Proc. of a Conference at Monash University (1–4 August, 1979), Upside Down A Book Company, Steele's Creek, Box 226, Yarra Glenn, Victoria, Australia, 1981.

    Google Scholar 

  2. Crossley, J. N., and Nerode, A., Combinatorial Functors, (monograph), Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 81, Springer-Verlag, New York, 1974.

    Book  MATH  Google Scholar 

  3. Dekker, J. C. E., "A Non-Constructive Extension of the Number System" (two abstracts), J. Symb. Logic 20 (1955), 204–205.

    Google Scholar 

  4. Dekker, J. C. E., Les Functions Combinatoires et Les Isols, Collection de Logique Mathematique ser. A. No. 22, Gauthier-Villars, Paris, 1966.

    MATH  Google Scholar 

  5. Dekker, J. C. E., and Myhill, J., "Recursive Equivalence Types", Univ. of California Publications in Mathematics n.s. 3 (1959), 67–214.

    MathSciNet  MATH  Google Scholar 

  6. Ellentuck, E., "The Universal Properties of Dedekind Finite Cardinals", Ann. Math. 82 (1965), 225–248.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ellentuck, E., "Generalized Idempotence in Cardinal Arithmetic", Fund. Math. 58 (1966),225–248.

    MathSciNet  MATH  Google Scholar 

  8. Ellentuck, E., "The First Order Properties of Dedekind Finite Integers", Fund. Math. 63, (1966), 7–25.

    MathSciNet  MATH  Google Scholar 

  9. Ellentuck, E., "Almost Combinatorial Skolem Functions", J. Symb. Logic 35 (1970), 378–382.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ellentuck, E., "Non-Recursive Combinatorial Functions", Jour. Symb. Logic 37 (1972), 90–95.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ellentuck, E., "The Positive Properties of Isolic Integers", J. Symbolic Logic 37, (1972), 114–132.

    Article  MathSciNet  MATH  Google Scholar 

  12. Friedberg, R.M., "The Uniqueness of Finite Division for Recursive Equivalence Types", Math. Z. 75 (1961), 3–7.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hay, L., "The Co-Simple Isols", Ann. Math. 83 (1966), 231–256.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hay, L., "Elementary Differences Between the Isols and the Co-Simple Isols", Trans. Amer. Math. Soc. 127 (1967), 427–441.

    Article  MathSciNet  MATH  Google Scholar 

  15. Hopcroft, J. E., and Ullman, J. D., Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass, 1979.

    MATH  Google Scholar 

  16. McCarty, D. C., Realizability and Recursive Mathematics, D. Phil dissertation, Oxford, 1980.

    Google Scholar 

  17. McLaughlin, T., Regressive Sets and the Theory of Isols, Marcel Dekker, New York, 1983.

    MATH  Google Scholar 

  18. Myhill, J., "Recursive Equivalence Types and Combinatorial Functions", Bull. Amer. Math. Soc. 64 (1958), 373–376.

    Article  MathSciNet  MATH  Google Scholar 

  19. Myhill, J., "Absorption Laws in the Arithmetic of Recursive Equivalence Types", Notices. Amer. Math Soc. 6 (1959), 526–527.

    Google Scholar 

  20. Nerode, A., "Extensions to Isols", Ann. of Math. 73 (1961), 362–403.

    Article  MathSciNet  MATH  Google Scholar 

  21. Nerode, A., "Extensions to Isolic Integers", Ann. of Math. 75 (1962), 419–448.

    Article  MathSciNet  MATH  Google Scholar 

  22. Nerode, A., "Non-Linear Combinatorial Functions of Isols", Math. Z. 86 (1965), 410–424.

    Article  MathSciNet  MATH  Google Scholar 

  23. Nerode, A., "Additive Relations Among Recursive Equivalence Types", Math. Ann. 159 (1965), 329–343.

    Article  MathSciNet  MATH  Google Scholar 

  24. Nerode, A., "Combinatorial Series and Recursive Equivalence Types", Fund. Math. 58 (1966), 133–141.

    MathSciNet  MATH  Google Scholar 

  25. Nerode, A., "Additive Relations among Recursive Equivalence Types", Math. Ann. 159 (1965), 329–343.

    Article  MathSciNet  MATH  Google Scholar 

  26. Nerode, A., "Diophantine Correct Non-Standard Models in the Isols", Ann. of Math. 84 (1966), 421–432.

    Article  MathSciNet  MATH  Google Scholar 

  27. Nerode, A., "Combinatorial Series and Recursive Equivalence Types", Fund. Math. 58 (1966), 133–141.

    MathSciNet  MATH  Google Scholar 

  28. Nerode, A., and Remmel, J. B., "A Survey of R. E. Substructures", Proc. Symp. in Pure Mathematics vol. 42, Amer. Math. Soc., 1985, 323–373.

    Article  MathSciNet  MATH  Google Scholar 

  29. Nerode, A. and Remmel, J. B., "Complexity-Theoretic Algebra 1: Vector Spaces over Finite Fields", Structure in Complexity (2nd Annual Conference), Computer Society of IEEE, 1987, 218–241.

    Google Scholar 

  30. Nerode, A., and Remmel, J. B., "Complexity-Theoretic Algebra II: Boolean Algebras", Proc. Third Asian Logic and Computer Science Symposium, Beijing 1987, Ann. of Pure and Applied Logic, to appear.

    Google Scholar 

  31. Nerode, A. and Remmel, J. B., "Polynomial Time Equivalence Types", CMU 1987 Logic and Computation Workshop volume, Contemporary Mathematics series, Amer Math. Soc., 1989, to appear.

    Google Scholar 

  32. Remmel, J. B., "Combinatorial Functors on Co-R. E. Structures", Ann. Math. Logic 11 (1976), 281–287.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Klaus Ambos-Spies Gert H. Müller Gerald E. Sacks

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Nerode, A., Remmel, J.B. (1990). Polynomially isolated sets. In: Ambos-Spies, K., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086125

Download citation

  • DOI: https://doi.org/10.1007/BFb0086125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52772-5

  • Online ISBN: 978-3-540-47142-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics