Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-02T18:16:32.328Z Has data issue: false hasContentIssue false

Hartley Rogers’ 1965 Agenda

Published online by Cambridge University Press:  31 March 2017

S. Barry Cooper
Affiliation:
University of Leeds
Samuel R. Buss
Affiliation:
University of California, San Diego
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Pavel Pudlák
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Get access
Type
Chapter
Information
Logic Colloquium '98 , pp. 154 - 172
Publisher: Cambridge University Press
Print publication year: 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. K., Ambos-Spies [1983], Automorphism bases for the r.e. degrees (abstract), in Extended Abstracts of Short Talks of the 1982 Summer Institute on Recursion Theory Held at Cornell University (I. Kalantari, ed.), special publication of Recursive Function Theory Newsletter, pp. 3–4.
2. W., Calhoun and T. A., Slaman [1996], The π0 2 e-degrees are not dense, J. Symbolic Logic 61, 1364–1379.Google Scholar
3. J., Case [1971], Enumeration reducibility and partial degrees, Ann. Math. Logic 2, 419–439.Google Scholar
4. P., Cholak [1995], Automorphisms of the Lattice of Recursively Enumerable Sets, Memoirs Amer. Math. Soc., Vol. 113, No. 541.Google Scholar
5. A., Church [1936], A note on the Entscheidungsproblem, J. Symbolic Logic 1, 40–41 and 101–102.Google Scholar
6. S. B., Cooper [1990a], The jump is definable in the structure of the degrees of unsolvability, Bull. Amer. Math. Soc. 23, 151–158.Google Scholar
7. S. B., Cooper [1990b], Enumeration reducibility, nondeterministic computations and relative computability of partial function, in Recursion TheoryWeek, Oberwolfach 1989 (K., Ambos-Spies, G., Müller, G. E., Sacks, eds.), Springer-Verlag, Berlin, Heidelberg, New York, 57–110.
8. S. B., Cooper [1994], Rigidity and definability in the non-computable universe, Logic,Methodology and Philosophy of Science IX, Proceedings of the Ninth InternationalCongress of Logic, Methodology and Philosophy of Science, Uppsala, Sweden, August 7–14,1991 (D., Prawitz, B., Skyrms and D., Westerstahl, eds.), North-Holland, Amsterdam, Lausanne, New York, Oxford, Shannon, Tokyo, pp. 209–236.
9. S. B., Cooper [1997], Beyond Gödel's Theorem: The failure to capture information content, in Complexity, Logic and Recursion Theory (A., Sorbi, ed.), Lecture Notes in Pure and Applied Mathematics, vol. 187, Marcel Dekker, New York, pp. 93–122.
10. S. B., Cooper [1999], Clockwork or Turing U/universe? – remarks on causal determinism and computability, in Models and Computability (S. B., Cooper and J. K., Truss, eds.), London Mathematical Society Lecture Note Series 259, Cambridge University Press, pp. 63–116.
11. C. S., Copestake [1988], 1-genericity in the enumeration degrees, J. Symbolic Logic 53, 878–887.Google Scholar
12. R. G., Downey and R. A., Shore [1997], There is no degree invariant half-jump, Proc. Amer. Math. Soc. 125, 3033–3037.Google Scholar
13. E. Z., Dyment [1976], Certain properties of the Medvedev lattice,Matmatičeskiî Sbornik 101 (143), 360–379 (Russian); Math. Notes 30, 321–340 (English tr.).Google Scholar
14. L., Feiner [1970], The strong homogeneity conjecture, J. Symbolic Logic 35, 375–377.Google Scholar
15. R. M., Friedberg and H., Rogers, Jr. [1959], Reducibility and completeness for sets of integers, Z. Math. Logik Grundlag.Math. 5, 117–125.Google Scholar
16. L., Gutteridge [1971], Some Results on Enumeration Reducibility, Ph.D. Dissertation, Simon Fraser University.
17. L. A., Harrington and A., Nies [1998], Coding in the partial order of enumerable sets, Adv. Math. 133, 133–162.Google Scholar
18. L. A., Harrington and R. I., Soare [1996], Definability, automorphisms, and dynamic properties of computably enumerable sets, Bull. Symbolic Logic 2, 199–213.Google Scholar
19. E., Herrmann [1984], The undecidability of the elementary theory of the lattice of recursively enumerable sets (abstract), in Frege Conference 1984, Proceedings of the International Conference at Schwerin, GDR, Akademie-Verlag, Berlin, pp. 66–72.
20. C. G., Jockusch, Jr. [1968], Uniformly introreducible sets, J. Symbolic Logic 33, 521–536.Google Scholar
21. C. G., Jockusch, Jr. and D., Posner [1981], Automorphism bases for degrees of unsolvability, Israel J. Math. 40, 150–164.Google Scholar
22. C. G., Jockusch, Jr. and R. A., Shore [1984], Pseudo jump operators II: Transfinite iterations, hierarchies, and minimal covers, J. Symbolic Logic 49, 1205–1236.Google Scholar
23. C. G., Jockusch, Jr. and S. G., Simpson [1976], A degree theoretic definition of the ramified analytical hierarchy, Ann. Math. Logic 10, 1–32.Google Scholar
24. C. F., Kent [1962], Constructive analogues of the group of permutations of the natural numbers, Trans. Amer. Math. Soc. 104, 347–362.Google Scholar
25. T. S., Kuhn [1962], The Structure of Scientific Revolutions (Third edition 1996), University of Chicago Press, Chicago, London.
26. A. H., Lachlan [1968a], Degrees of recursively enumerable sets which have no maximal superset, J. Symbolic Logic 33, 431–443.Google Scholar
27. M., Lerman [1983], Degrees of Unsolvability, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Berlin, Heidelberg, London, New York, Tokyo.
28. D. A., Martin [1966], Classes of recursively enumerable sets and degrees of unsolvability, Z. Math. Logik Grundlag.Math. 12, 295–310.Google Scholar
29. D. A., Martin [1968], The axiom of determinateness and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74, 687–689.Google Scholar
30. K., McEvoy [1984], The Structure of the Enumeration Degrees, Ph.D. thesis, University of Leeds.
31. Yu. T., Medvedev [1955], Degrees of difficulty of the mass problem, Dokl. Akad. Nauk SSSR N.S. 104, 501–504 (Russian).
32. J., Myhill [1955], Creative sets, Z. Math. Logik Grundlag.Math. 1, 97–108.Google Scholar
33. A., Nerode and R. A., Shore [1980a], Second order logic and first order theories of reducibility orderings, in The Kleene Symposium (J., Barwise et al., eds.), North-Holland, Amsterdam, pp. 181-200.
34. A., Nerode and R. A., Shore [1980b], Reducibility orderings: theories, definability and automorphisms, Ann. Math. Logic 18, 61–89.Google Scholar
35. A., Nies [1997], Intervals of the lattice of computably enumerable sets and effective Boolean algebras, Bull. London Math. Soc. 29, 683–692.Google Scholar
36. A., Nies, R. A., Shore, T. A., Slaman [1996], Definability in the recursively enumerable degrees, Bull. Symbolic Logic 2, 392–404.Google Scholar
37. A., Nies, R. A., Shore, T. A., Slaman [1998], Interpretability and definability in the recursively enumerable degrees, Proc. London Math. Soc. (3) 77, 241–291.Google Scholar
38. P., Odifreddi [1989], Classical Recursion Theory, North-Holland, Amsterdam, New York, Oxford.
39. P., Odifreddi [ta1], Reducibilities, to appear in The Handbook of Computability Theory (E., Griffor, ed.), North-Holland, Amsterdam, New York, Oxford.
40. P., Odifreddi [ta2], Classical Recursion Theory, Vol. II, North-Holland, Amsterdam, New York, Oxford, to appear.
41. E. L., Post [1944], Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. 50, 284–316.Google Scholar
42. E. L., Post [1948], Degrees of unsolvability: preliminary report (abstract), Bull. Amer.Math. Soc. 54, 641–642.Google Scholar
43. H., Rogers, Jr. [1967a], Some problems of definability in recursive function theory, in Sets, Models and Recursion Theory (J. N., Crossley, ed.), Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September, 1965, North Holland, Amsterdam, pp. 183–201.
44. H., Rogers, Jr. [1967b], Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York.
45. M., Rozinas [1978], The semi-lattice of e-degrees, in Recursive Functions, Ivanov.Gos. Univ., Ivanovo, 71–84 (Russian).
46. G. E., Sacks [1963], On the degrees less than 0, Ann. of Math. (2) 77, 211–231.Google Scholar
47. G. E., Sacks [1966], Degrees of Unsolvability (revised edition), Ann. of Math. Studies No. 55, Princeton University Press, Princeton, N.J.
48. G. E., Sacks [1985], Some open questions in recursion theory, in Recursion Theory Week (H. D., Ebbinghaus, G. H., Müuller and G. E., Sacks, eds.), Proceedings of a Conference held in Oberwolfach, West Germany, April 15-21, 1984, Lecture Notes in Mathematics No. 1141, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, pp. 333-342.
49. A. L., Selman [1971], Arithmetical reducibilities I, Z. Math. Logik Grundlag. Math. 17, 335–350.Google Scholar
50. J. R., Shoenfield [1976], Degrees of classes of r.e. sets, J. Symbolic Logic 41, 695–696.Google Scholar
51. R. A., Shore [1981], The theory of the degrees below 0, J. London Math. Soc. (2) 24, 1–14.Google Scholar
52. S.G., Simpson [1977], First-order theory of the degrees of recursive unsolvability, Ann.of Math. (2) 105, 121–139.Google Scholar
53. T. A., Slaman [1991], Degree structures, in Proceedings of the International Congress of Mathematicians, Kyoto, 1990, Springer-Verlag, Berlin, Heidelberg, London, New York, Tokyo, pp. 303–316.
54. T. A., Slaman and W. H., Woodin [1997], Definability in the enumeration degrees Arch.Math. Logic 36, 255–267.Google Scholar
55. R. I., Soare [1974a], Automorphisms of the lattice of recursively enumerable sets, Bull.Amer. Math. Soc. 80, 53–58.Google Scholar
56. R. I., Soare [1974b], Automorphisms of the lattice of recursively enumerable sets, Part I: Maximal sets, Ann. Math. (2) 100, 80–120.Google Scholar
57. R. I., Soare [1987], Recursively Enumerable Sets and Degrees, Springer-Verlag, Berlin, Heidelberg, London, New York.
58. A., Sorbi [1990], Some remarks on the algebraic structure of the Medvedev lattice, J. Symbolic Logic 55, 831–853.Google Scholar
59. A., Sorbi [1996], The Medvedev lattice of degrees of difficulty, in Computability, Enumerability,Unsolvability: Directions in Recursion Theory (S. B., Cooper, T. A., Slaman and S. S., Wainer, eds.), London Mathematical Society Lecture Note Series 224, Cambridge University Press, Cambridge, 289–312.
60. A., Sorbi [1998], Sets of generators and automorphism bases for the enumeration degrees Ann. Pure and Applied Logic 94, 263–272.Google Scholar
61. A. M., Turing [1936], On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. 42, 230–265.Google Scholar
62. A. M., Turing [1939], Systems of logic based on ordinals, Proc. London Math. Soc. 45, 161–228; reprinted in The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions (M., Davis, ed.), Raven Press, New York, 1965, pp. 154–222.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×