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Local Initial Segments of The Turing Degrees

  • Bjørn Kjos-Hanssen (a1)
Abstract
Abstract

Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of the Turing degrees are indicated.

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[1] U. Abraham and R. A. Shore , Initial segments of the degrees of size 풩1, Israel Journal of Mathematics, vol. 53 (1986), no. 1, pp. 151.

[2] G. Gierz et al, A compendium of continuous lattices, Springer Verlag, 1980.

[5] M. J. Groszek and T. A. Slaman , Independence results on the global structure of the Turing degrees, Transactions of the American Mathematical Society, vol. 277 (1983), pp. 579587.

[9] A. H. Lachlan , Solution to a problem of Spector, Canadian Journal of Mathematics, vol. 23 (1971), pp. 247256.

[10]; A. H. Lachlan and R. Lebeuf , Countable initial segments of the degrees, The Journal of Symbolic Logic, vol. 41 (1976), pp. 289300.

[11] M. Lerman , Initial segments of the degrees of unsolvability, Annals of Mathematics (2), vol. 93 (1971), pp. 311389.

[12] M. Lerman , Degrees of unsolvability, Perspectives in Mathematical Logic, Springer-Verlag, Heidelberg, 1983.

[15] W. Miller and D. A. Martin , The degrees of hyperimmune sets, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 14 (1968), pp. 159166.

[17] P. Pudlák , A new proof of the congruence lattice representation theorem, Algebra Universalis, vol. 6 (1976), pp. 269275.

[18] G. E. Sacks , A minimal degree below 0′, Bulletin of the American Mathematical Society, vol. 67 (1961), pp. 416419.

[19] R.A. Shore , Defining jump classes in the degrees below 0′, Proceedings of the American Mathematical Society, vol. 104 (1988), no. 1, pp. 287292.

[20] R. A. Shore and T. A. Slaman , Defining the Turing jump, Mathematical Research Letters, vol. 6 (1999), no. 5–6, pp. 711722.

[22] C. Spector , On the degrees of recursive unsolvability, Annals of Mathematics (2), vol. 64 (1956), pp. 581592.

[23] P.M. Whitman , Lattices, equivalence relations and subgroups, Bulletin of the American Mathematical Society, vol. 52 (1946), pp. 507522.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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