Trees and degrees

  • Piergiorgio Odifreddi
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 839)


Minimal Degree Initial Segment Recursive Function Recursive Partition Recursive Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. S. B. Cooper [1973], Minimal degrees and the jump operator, J. Symb. Logic 38 (1973), 249–271.MathSciNetCrossRefzbMATHGoogle Scholar
  2. R. L. Epstein [1975], Minimal degrees of unsolvability and the full approximation method, Memoirs AMS 162 (1975).Google Scholar
  3. R. L. Epstein [1979], Degrees of unsolvability: Structure and theory, Lecture Notes 759, Springer (1979).Google Scholar
  4. D. F. Hugill [1969], Initial segments of Turing degrees, Proc. London Math. Soc. 19 (1969), 1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  5. C. Jockusch [1969a], Relationships between reducibilities, Trans. AMS 142, (1969), 229–237.MathSciNetCrossRefzbMATHGoogle Scholar
  6. C. Jockusch [1969b], The degrees of bi-immune sets, Zeit. Math. Logic. Grund. Math. 15 (1969), 135–140.MathSciNetCrossRefzbMATHGoogle Scholar
  7. C. Jockusch [1972], Ramsey’s theorem and recursion theory, J. Symb. Logic 37 (1972), 268–280.MathSciNetCrossRefzbMATHGoogle Scholar
  8. C. Jockusch [1977], Simple proofs of some theorems on high degrees, Can. J. Math. 29 (1977), 1072–1080.MathSciNetCrossRefzbMATHGoogle Scholar
  9. C. Jockusch and M. S. Paterson [1976], Completely autoreducible degrees, Zeit. Math. Logic Grund. Math. 22 (1976), 571–575.MathSciNetCrossRefzbMATHGoogle Scholar
  10. C. Jockusch and D. Posner [1978], Double jumps of minimal degrees, J. Symb. Logic 43 (1978), 715–724.MathSciNetCrossRefzbMATHGoogle Scholar
  11. C. Jockusch and D. Posner [198?], Automorphism bases for the degrees of unsolvability, to appear.Google Scholar
  12. C. Jockusch and S. Simpson [1975], A degree-theoretic definition of the ramified analytic hierarchy, Ann. of Math. Logic 10 (1975), 1–32.MathSciNetCrossRefzbMATHGoogle Scholar
  13. C. Jockusch and R. Soare [1972a], Degrees of members of Π10 classes, Pac. J. Math. 40 (1972), 605–616.MathSciNetCrossRefzbMATHGoogle Scholar
  14. C. Jockusch and R. Soare [1972b], Π10 classes and degrees of theories, Trans. AMS 173 (1972), 33–56.MathSciNetzbMATHGoogle Scholar
  15. S. C. Kleene and E. L. Post [1954], The upper-semilattice of degrees of recursive unsolvability, Ann. of Math. 59 (1954), 379–407.MathSciNetCrossRefzbMATHGoogle Scholar
  16. A. H. Lachlan [1968], Distributive initial segments of the degrees of unsolvability, Zeit. Math. Logic. Grund. Math. 14 (1968), 457–472.MathSciNetCrossRefzbMATHGoogle Scholar
  17. A. H. Lachlan [1971], Solution to a problem of Spector, Can. J. Math. 23 (1971), 247–256.MathSciNetCrossRefzbMATHGoogle Scholar
  18. A. H. Lachlan and R. Lebeuf [1976], Countable initial segments of the degrees of unsolvability, J. Symb. Logic 41 (1976), 289–300.MathSciNetCrossRefzbMATHGoogle Scholar
  19. R. Ladner [1973], A completely mitotic non recursive r.e. set, Trans. AMS 184 (1973), 479–507.MathSciNetCrossRefzbMATHGoogle Scholar
  20. M. Lerman [1969], Some non distributive lattices as initial segments of the degrees of unsolvability, J. Symb. Logic 34 (1969), 85–98.MathSciNetCrossRefzbMATHGoogle Scholar
  21. M. Lerman [1971], Initial segments of the degrees of unsolvability, Ann. of Math. 93 (1971), 365–389.MathSciNetCrossRefzbMATHGoogle Scholar
  22. A. B. Manaster [1971], Some contrasts between degrees and the arithmetical hierarchy, J. Symb. Logic 36 (1971), 301–304.MathSciNetCrossRefzbMATHGoogle Scholar
  23. D. A. Martin and W. Miller [1968], The degrees of hyperimmune sets, Zeit. Math. Logic Grund. Math. 14 (1968), 159–166.MathSciNetCrossRefzbMATHGoogle Scholar
  24. A. Nerode and R. A. Shore [198?], Second order logic and first order theories of reducibility orderings, to appear.Google Scholar
  25. P. G. Odifreddi [198?], Classical recursion theory, to appear.Google Scholar
  26. D. Posner and R. Epstein [1978], Diagonalization in degree constructions, J. Symb. Logic 43 (1978), 280–283.MathSciNetCrossRefzbMATHGoogle Scholar
  27. E. L. Post [1944], Recursively enumerable sets of positive integers and their decision problems, Bull. AMS 50 (1944), 284–316.MathSciNetCrossRefzbMATHGoogle Scholar
  28. H. Rogers, Jr. [1967], The theory of recursive functions and effective computability, McGraw-Hill, 1967.Google Scholar
  29. G. E. Sacks [1961], A minimal degree less than O’, Bull. AMS 67 (1961), 416–419.MathSciNetCrossRefzbMATHGoogle Scholar
  30. G. E. Sacks [1963], Degrees of unsolvability, Ann. Math. Studies n.55, Princeton, 1963.Google Scholar
  31. G. E. Sacks [1971], Forcing with perfect closed sets, Proc. Symp. Pure Math. 13 (1971), 331–355.MathSciNetCrossRefzbMATHGoogle Scholar
  32. L. Sasso [1970], A cornucopia of minimal degrees, J. Symb. Logic. 35 (1970), 383–388.MathSciNetCrossRefzbMATHGoogle Scholar
  33. L. Sasso [1974], A minimal degree not realizing the least possible jump, J. Symb. Logic 39 (1974), 571–573.MathSciNetCrossRefzbMATHGoogle Scholar
  34. J. R. Shoenfield [1966], A theorem on minimal degrees, J. Symb. Logic 31 (1966), 539–544.MathSciNetCrossRefzbMATHGoogle Scholar
  35. E. Specker [1971], Ramsey’s theorem does not hold in recursive set theory, Logic Colloquium ’69, North Holland 1971, 439–442.Google Scholar
  36. C. Spector [1956], On degrees of recursive unsolvability, Ann. of Math. 65 (1956), 581–592.MathSciNetCrossRefzbMATHGoogle Scholar
  37. D. Titgemeyer [1965], Untersuchungen über die struktur des Kleene-Postchen Halbverbandes der Grade der rekursiven Unlösbarkeit, Arch. Math. Logic Grund. 8 (1965), 45–62.MathSciNetCrossRefzbMATHGoogle Scholar
  38. Trathenbrot [1970], On autoreducibility, Sov. Math. Dokl. 11 (1970), 814–817.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Piergiorgio Odifreddi
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaLos Angeles
  2. 2.Istituto MatematicoUniversità di TorinoTorinoItaly

Personalised recommendations