Israel Journal of Mathematics

, Volume 26, Issue 1, pp 91–94 | Cite as

Fixed points of jump preserving automorphisms of degrees

  • Carl G. Jockusch
  • Robert M. Solovay


It is shown that any jump preserving order automorphismF of the degrees of unsolvability must satisfyF(c) = c for all degreesc≧0 (4) . The proof uses a result on initial segments of degrees in combination with an iteration of the Friedberg completeness criterion.


Distributive Lattice Initial Segment Direct Appeal WATSON Research Infinite Domain 
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  1. 1.
    R. M. Friedberg,A criterion for completeness of degrees of unsolvability, J. Symbolic Logic22 (1957), 159–160.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. H. Lachlan,Distributive initial segments of the degrees of unsolvability, Z. Math. Logik. Grundlagen Math.14 (1968), 457–472.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    A. H. Lachlan and R. Lebeuf,Countable initial segments of the degrees of unsolvability, J. Symbolic Logic41 (1976), 289–300.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A. L. Selman,Applications of forcing to the degree-theory of the arithmetical hierarchy, Proc. London Math. Soc.25 (3) (1972), 586–602.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    C. E. M. Yates,Initial segments and implications for the structure of degrees, inConference in Mathematical Logic-London 1970 (Lecture Notes in Mathematics Vol. 255), Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 305–335.Google Scholar

Copyright information

© Hebrew University 1977

Authors and Affiliations

  • Carl G. Jockusch
    • 1
    • 2
  • Robert M. Solovay
    • 1
    • 2
  1. 1.University of Illinois at Urbana-ChampaignUSA
  2. 2.I.B.M. T. J. Watson Research CenterUSA

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