메뉴 건너뛰기




Volumn 140, Issue C, 1999, Pages 169-197

Chapter 6 The recursively enumerable degrees

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0013416239     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(99)80022-6     Document Type: Chapter
Times cited : (11)

References (93)
  • 1
    • 0003412508 scopus 로고
    • On the structure of the recursively enumerable degrees
    • University of Munich
    • Ambos-Spies K. On the structure of the recursively enumerable degrees. Ph.D. Thesis (1980), University of Munich
    • (1980) Ph.D. Thesis
    • Ambos-Spies, K.1
  • 2
    • 77956949236 scopus 로고
    • Generators of the recursively enumerable degrees
    • Recursion Theory Week, Proceedings. Ebbinghaus H.-D., Müller G.H., and Sacks G.E. (Eds). Oberwolfach 1984, Springer, Berlin
    • Ambos-Spies K. Generators of the recursively enumerable degrees. In: Ebbinghaus H.-D., Müller G.H., and Sacks G.E. (Eds). Recursion Theory Week, Proceedings. Oberwolfach 1984. Lecture Notes in Mathematics Vol. 1141 (1985), Springer, Berlin 1-28
    • (1985) Lecture Notes in Mathematics , vol.1141 , pp. 1-28
    • Ambos-Spies, K.1
  • 5
    • 0030494882 scopus 로고    scopus 로고
    • Decidability of the two-quantifier theory of the recursively enumerable weak truth-table degrees and other distributive upper semi-lattices
    • Ambos-Spies K., Fejer P.A., Lempp S., and Lerman M. Decidability of the two-quantifier theory of the recursively enumerable weak truth-table degrees and other distributive upper semi-lattices. J. Symbolic Logic 61 (1996) 880-905
    • (1996) J. Symbolic Logic , vol.61 , pp. 880-905
    • Ambos-Spies, K.1    Fejer, P.A.2    Lempp, S.3    Lerman, M.4
  • 7
    • 77956950368 scopus 로고
    • Lattice embeddings into the r.e. degrees preserving 1
    • Prawitz D., and Westerahl D. (Eds), Kluwer Academic Publishers, Dordrecht
    • Ambos-Spies K., Lempp S., and Lerman M. Lattice embeddings into the r.e. degrees preserving 1. In: Prawitz D., and Westerahl D. (Eds). Logic and Philosophy of Science: Papers from the 9th ICLMPS (1994), Kluwer Academic Publishers, Dordrecht 179-198
    • (1994) Logic and Philosophy of Science: Papers from the 9th ICLMPS , pp. 179-198
    • Ambos-Spies, K.1    Lempp, S.2    Lerman, M.3
  • 8
    • 0009887506 scopus 로고
    • Lattice embeddings into the r.e. degrees preserving 0 and 1
    • Ambos-Spies K., Lempp S., and Lerman M. Lattice embeddings into the r.e. degrees preserving 0 and 1. J. London Math. Soc. 49 2 (1994) 1-15
    • (1994) J. London Math. Soc. , vol.49 , Issue.2 , pp. 1-15
    • Ambos-Spies, K.1    Lempp, S.2    Lerman, M.3
  • 9
    • 0000741451 scopus 로고
    • Lattice embeddings into the recursively enumerable degrees
    • Ambos-Spies K., and Lerman M. Lattice embeddings into the recursively enumerable degrees. J. Symbolic Logic 51 (1986) 257-272
    • (1986) J. Symbolic Logic , vol.51 , pp. 257-272
    • Ambos-Spies, K.1    Lerman, M.2
  • 10
    • 0000334677 scopus 로고
    • Lattice embeddings into the recursively enumerable degrees II
    • Ambos-Spies K., and Lerman M. Lattice embeddings into the recursively enumerable degrees II. J. Symbolic Logic 54 (1989) 735-760
    • (1989) J. Symbolic Logic , vol.54 , pp. 735-760
    • Ambos-Spies, K.1    Lerman, M.2
  • 11
    • 0040456551 scopus 로고
    • Undecidability and 1-types in the r.e. degrees
    • Ambos-Spies K., and Shore R.A. Undecidability and 1-types in the r.e. degrees. Ann. Pure Appl. Logic 63 (1993) 3-37
    • (1993) Ann. Pure Appl. Logic , vol.63 , pp. 3-37
    • Ambos-Spies, K.1    Shore, R.A.2
  • 12
    • 38249004715 scopus 로고
    • The recursively enumerable degrees have infinitely many one-types
    • Ambos-Spies K., and Soare R.I. The recursively enumerable degrees have infinitely many one-types. Ann. Pure Appl. Logic 44 (1989) 1-23
    • (1989) Ann. Pure Appl. Logic , vol.44 , pp. 1-23
    • Ambos-Spies, K.1    Soare, R.I.2
  • 13
    • 0010749665 scopus 로고
    • Characterization of jump operators
    • Becker H.A. Characterization of jump operators. J. Symbolic Logic 53 (1988) 708-728
    • (1988) J. Symbolic Logic , vol.53 , pp. 708-728
    • Becker, H.A.1
  • 14
    • 38249002873 scopus 로고
    • Lattice nonembeddings and intervals of the recursively enumerable degrees
    • Cholak P., and Downey R.G. Lattice nonembeddings and intervals of the recursively enumerable degrees. Ann. Pure Appl. Logic 61 (1993) 195-221
    • (1993) Ann. Pure Appl. Logic , vol.61 , pp. 195-221
    • Cholak, P.1    Downey, R.G.2
  • 15
    • 0346447069 scopus 로고    scopus 로고
    • Intervals without critical triples
    • Logic Colloquium '95. Makowsky J.A., and Ravve E.V. (Eds), Springer, Heidelberg
    • Cholak P., Downey R.G., and Shore R.A. Intervals without critical triples. In: Makowsky J.A., and Ravve E.V. (Eds). Logic Colloquium '95. Lecture Notes in, Logic vol. 11 (1998), Springer, Heidelberg 17-43
    • (1998) Lecture Notes in, Logic , vol.11 , pp. 17-43
    • Cholak, P.1    Downey, R.G.2    Shore, R.A.3
  • 16
    • 0001117413 scopus 로고
    • Minimal pairs and high recursively enumerable degrees
    • Cooper S.B. Minimal pairs and high recursively enumerable degrees. J. Symbolic Logic 39 (1974) 655-660
    • (1974) J. Symbolic Logic , vol.39 , pp. 655-660
    • Cooper, S.B.1
  • 17
    • 84968488123 scopus 로고
    • The jump is definable in the structure of the degrees of unsolvability (research announcement)
    • Cooper S.B. The jump is definable in the structure of the degrees of unsolvability (research announcement). Bull. Amer. Math. Soc. 23 (1990) 151-158
    • (1990) Bull. Amer. Math. Soc. , vol.23 , pp. 151-158
    • Cooper, S.B.1
  • 20
    • 38249018607 scopus 로고
    • Lattice nonembeddings and initial segments of the recursively enumerable degrees
    • Downey R.G. Lattice nonembeddings and initial segments of the recursively enumerable degrees. Ann. Pure Appl. Logic 49 (1990) 97-119
    • (1990) Ann. Pure Appl. Logic , vol.49 , pp. 97-119
    • Downey, R.G.1
  • 21
    • 0000448889 scopus 로고
    • Notes on the O‴ priority method with special attention to density results
    • Recursion Theory Week. Ambos-Spies K., and Müller G.H. (Eds), Springer, Berlin
    • Downey R.G. Notes on the O‴ priority method with special attention to density results. In: Ambos-Spies K., and Müller G.H. (Eds). Recursion Theory Week. Lecture Notes in Mathematics Vol. 1432 (1990), Springer, Berlin 111-140
    • (1990) Lecture Notes in Mathematics , vol.1432 , pp. 111-140
    • Downey, R.G.1
  • 22
    • 0031316605 scopus 로고    scopus 로고
    • Contiguity and distributivity in the enumerable Turing degrees
    • Downey R.G., and Lempp S. Contiguity and distributivity in the enumerable Turing degrees. J. Symbolic Logic 62 (1997) 1215-1240
    • (1997) J. Symbolic Logic , vol.62 , pp. 1215-1240
    • Downey, R.G.1    Lempp, S.2
  • 25
    • 0010667032 scopus 로고    scopus 로고
    • There is no degree invariant half-jump
    • Downey R.G., and Shore R.A. There is no degree invariant half-jump. Proc. Amer. Math. Soc. 125 (1997) 3033-3037
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 3033-3037
    • Downey, R.G.1    Shore, R.A.2
  • 26
    • 0038292941 scopus 로고
    • The density of the nonbranching degrees
    • Fejer P.A. The density of the nonbranching degrees. Ann. Pure Appl. Logic 24 (1983) 113-130
    • (1983) Ann. Pure Appl. Logic , vol.24 , pp. 113-130
    • Fejer, P.A.1
  • 27
    • 0000857719 scopus 로고
    • Two recursively enumerable sets of incomparable degrees of unsolvability
    • Friedberg R.M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc. Nat. Acad. Sci. 43 (1957) 236-238
    • (1957) Proc. Nat. Acad. Sci. , vol.43 , pp. 236-238
    • Friedberg, R.M.1
  • 28
    • 84966206129 scopus 로고
    • The undecidability of the recursively enumerable degrees (research announcement)
    • Harrington L., and Shelah S. The undecidability of the recursively enumerable degrees (research announcement). Bull. Amer. Math. Soc., (N.S.) 6 (1982) 79-80
    • (1982) Bull. Amer. Math. Soc., (N.S.) , vol.6 , pp. 79-80
    • Harrington, L.1    Shelah, S.2
  • 29
    • 0025721105 scopus 로고
    • Post's program and incomplete recursively enumerable sets
    • Harrington L., and Soare R.I. Post's program and incomplete recursively enumerable sets. Proc. Nat. Acad. Sci. 88 (1991) 10242-10246
    • (1991) Proc. Nat. Acad. Sci. , vol.88 , pp. 10242-10246
    • Harrington, L.1    Soare, R.I.2
  • 31
    • 0000755518 scopus 로고
    • Pseudo-jump operators II: Transfinite iterations, hierarchies and minimal covers
    • Jockusch Jr. C.G., and Shore R.A. Pseudo-jump operators II: Transfinite iterations, hierarchies and minimal covers. J. Symbolic Logic 49 (1984) 1205-1236
    • (1984) J. Symbolic Logic , vol.49 , pp. 1205-1236
    • Jockusch Jr., C.G.1    Shore, R.A.2
  • 32
    • 0001620455 scopus 로고
    • The upper semi-lattice of degrees of recursive unsolvability
    • Kleene S.C., and Post E. The upper semi-lattice of degrees of recursive unsolvability. Ann. Math. 59 2 (1954) 379-407
    • (1954) Ann. Math. , vol.59 , Issue.2 , pp. 379-407
    • Kleene, S.C.1    Post, E.2
  • 33
    • 0003451932 scopus 로고
    • Kechris A.S., and Moschovakis Y. (Eds), Springer, Berlin
    • In: Kechris A.S., and Moschovakis Y. (Eds). Cabal Seminar 76-77. Lecture Notes in Mathematics Vol. 689 (1978), Springer, Berlin
    • (1978) Lecture Notes in Mathematics , vol.689
  • 34
    • 85008722734 scopus 로고
    • Lower bounds for pairs of recursively enumerable degrees
    • Lachlan A.H. Lower bounds for pairs of recursively enumerable degrees. Proc. London Math. Soc. 16 (1966) 537-569
    • (1966) Proc. London Math. Soc. , vol.16 , pp. 537-569
    • Lachlan, A.H.1
  • 35
    • 0000288557 scopus 로고
    • The impossibility of finding relative complements for recursively enumerable degrees
    • Lachlan A.H. The impossibility of finding relative complements for recursively enumerable degrees. J. Symbolic Logic 31 (1966) 434-454
    • (1966) J. Symbolic Logic , vol.31 , pp. 434-454
    • Lachlan, A.H.1
  • 36
    • 84972500425 scopus 로고
    • The elementary theory of recursively enumerable sets
    • Lachlan A.H. The elementary theory of recursively enumerable sets. Duke Math. J. 35 (1968) 123-146
    • (1968) Duke Math. J. , vol.35 , pp. 123-146
    • Lachlan, A.H.1
  • 37
    • 0000365074 scopus 로고
    • Embedding nondistributive lattices in the recursively enumerable degrees
    • Conference in Mathematical Logic. Hodges W. (Ed). London, 1970, Springer, Berlin
    • Lachlan A.H. Embedding nondistributive lattices in the recursively enumerable degrees. In: Hodges W. (Ed). Conference in Mathematical Logic. London, 1970. Lecture Notes in Mathematics Vol. 255 (1972), Springer, Berlin 149-172
    • (1972) Lecture Notes in Mathematics , vol.255 , pp. 149-172
    • Lachlan, A.H.1
  • 38
    • 77956948539 scopus 로고
    • The priority method for the construction of recursively enumerable sets
    • Cambridge Summer School in Mathematical Logic. Mathias A.R.D., and Rogers Jr. H. (Eds), Springer, Berlin
    • Lachlan A.H. The priority method for the construction of recursively enumerable sets. In: Mathias A.R.D., and Rogers Jr. H. (Eds). Cambridge Summer School in Mathematical Logic. Lecture Notes in Mathematics Vol. 337 (1973), Springer, Berlin 299-310
    • (1973) Lecture Notes in Mathematics , vol.337 , pp. 299-310
    • Lachlan, A.H.1
  • 39
    • 0001617354 scopus 로고
    • A recursively enumerable degree which will not split over all lesser ones
    • Lachlan A.H. A recursively enumerable degree which will not split over all lesser ones. Ann. Math. Logic 9 (1975) 307-365
    • (1975) Ann. Math. Logic , vol.9 , pp. 307-365
    • Lachlan, A.H.1
  • 40
    • 0010749667 scopus 로고
    • Uniform enumeration operators
    • Lachlan A.H. Uniform enumeration operators. J. Symbolic Logic 40 (1975) 401-409
    • (1975) J. Symbolic Logic , vol.40 , pp. 401-409
    • Lachlan, A.H.1
  • 41
    • 84966203740 scopus 로고
    • Decomposition of recursively enumerable degrees
    • Lachlan A.H. Decomposition of recursively enumerable degrees. Proc. Amer. Math. Soc. 79 (1980) 629-634
    • (1980) Proc. Amer. Math. Soc. , vol.79 , pp. 629-634
    • Lachlan, A.H.1
  • 42
    • 0002319804 scopus 로고
    • Not every finite lattice is embeddable in the recursively enumerable degrees
    • Lachlan A.H., and Soare R.I. Not every finite lattice is embeddable in the recursively enumerable degrees. Adv. Math. 37 (1980) 74-82
    • (1980) Adv. Math. , vol.37 , pp. 74-82
    • Lachlan, A.H.1    Soare, R.I.2
  • 43
    • 0031572116 scopus 로고    scopus 로고
    • A finite lattice without critical triples that cannot be embedded into the enumerable Turing degrees
    • Lempp S., and Lerman M. A finite lattice without critical triples that cannot be embedded into the enumerable Turing degrees. Ann Pure Appl. Logic 87 (1997) 167-185
    • (1997) Ann Pure Appl. Logic , vol.87 , pp. 167-185
    • Lempp, S.1    Lerman, M.2
  • 44
    • 22044445793 scopus 로고    scopus 로고
    • 3 theory of the enumerable Turing degrees is undecidable
    • 3 theory of the enumerable Turing degrees is undecidable. Trans. Amer. Math. Soc. 350 (1998) 2719-2736
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 2719-2736
    • Lempp, S.1    Nies, A.2    Slaman, T.3
  • 47
    • 0010127118 scopus 로고    scopus 로고
    • Embeddings into the recursively enumerable degrees
    • Computability, Enumerability, Unsolvability: Directions in Recursion Theory. Cooper S.B., Slaman T.A., and Wainer S.S. (Eds), Cambridge University Press, Cambridge, UK
    • Lerman M. Embeddings into the recursively enumerable degrees. In: Cooper S.B., Slaman T.A., and Wainer S.S. (Eds). Computability, Enumerability, Unsolvability: Directions in Recursion Theory. LMSLNS Vol. 224 (1996), Cambridge University Press, Cambridge, UK 185-204
    • (1996) LMSLNS , vol.224 , pp. 185-204
    • Lerman, M.1
  • 48
    • 0032487282 scopus 로고    scopus 로고
    • A necessary and sufficient condition for embedding ranked finite lattices into the computably enumerable degrees
    • Lerman M. A necessary and sufficient condition for embedding ranked finite lattices into the computably enumerable degrees. Ann. Pure Appl. Logic 94 (1998) 143-180
    • (1998) Ann. Pure Appl. Logic , vol.94 , pp. 143-180
    • Lerman, M.1
  • 50
    • 84966216665 scopus 로고
    • Decidability and invariant classes for degree structures
    • Lerman M., and Shore R.A. Decidability and invariant classes for degree structures. Trans. Amer. Math. Soc. 310 (1988) 669-692
    • (1988) Trans. Amer. Math. Soc. , vol.310 , pp. 669-692
    • Lerman, M.1    Shore, R.A.2
  • 52
    • 0001296554 scopus 로고
    • Recursively enumerable generic sets
    • Maass W. Recursively enumerable generic sets. J. Symbolic Logic 47 (1982) 809-823
    • (1982) J. Symbolic Logic , vol.47 , pp. 809-823
    • Maass, W.1
  • 53
    • 0002176728 scopus 로고
    • High recursively enumerable degrees and the anti-cupping property
    • Logic Year 1979-1980: University of Connecticut. Lerman M., Schmerl J., and Soare R.I. (Eds), Springer, Berlin
    • Miller D. High recursively enumerable degrees and the anti-cupping property. In: Lerman M., Schmerl J., and Soare R.I. (Eds). Logic Year 1979-1980: University of Connecticut. Lecture Notes in Mathematics Vol. 859 (1981), Springer, Berlin 230-245
    • (1981) Lecture Notes in Mathematics , vol.859 , pp. 230-245
    • Miller, D.1
  • 54
    • 0001170426 scopus 로고
    • On the unsolvability of the problem of reducibility in the theory of algorithms
    • Muchnik A.A. On the unsolvability of the problem of reducibility in the theory of algorithms. Dokl. Akad. Nauk SSSR (N.S.) 108 (1956) 29-32
    • (1956) Dokl. Akad. Nauk SSSR (N.S.) , vol.108 , pp. 29-32
    • Muchnik, A.A.1
  • 55
    • 0011330069 scopus 로고
    • Solution of Post's reduction problem and of certain other problems in the theory of algorithms
    • Muchnik A.A. Solution of Post's reduction problem and of certain other problems in the theory of algorithms. Trudy Moskov Mat. Obsc. 7 (1958) 391-405
    • (1958) Trudy Moskov Mat. Obsc. , vol.7 , pp. 391-405
    • Muchnik, A.A.1
  • 56
    • 0030299478 scopus 로고    scopus 로고
    • Definability in the recursively enumerable degrees
    • Nies A., Shore R.A., and Slaman T. Definability in the recursively enumerable degrees. Bull. Symbolic Logic 2 (1996) 392-404
    • (1996) Bull. Symbolic Logic , vol.2 , pp. 392-404
    • Nies, A.1    Shore, R.A.2    Slaman, T.3
  • 57
    • 0009889489 scopus 로고    scopus 로고
    • Interpretability and definability in the recursively enumerable degrees
    • Nies A., Shore R.A., and Slaman T. Interpretability and definability in the recursively enumerable degrees. Proc. London Math. Soc. 77 3 (1998) 241-249
    • (1998) Proc. London Math. Soc. , vol.77 , Issue.3 , pp. 241-249
    • Nies, A.1    Shore, R.A.2    Slaman, T.3
  • 58
    • 0000350658 scopus 로고
    • Finite combinatory processes-formulation
    • Post E.L. Finite combinatory processes-formulation. J.Symbolic Logic 1 (1936) 103-105
    • (1936) J.Symbolic Logic , vol.1 , pp. 103-105
    • Post, E.L.1
  • 59
    • 0039109004 scopus 로고
    • Recursively enumerable sets of positive integers and their decision problems
    • Post E.L. Recursively enumerable sets of positive integers and their decision problems. Bull. Amer. Math. Soc. 50 (1944) 284-316
    • (1944) Bull. Amer. Math. Soc. , vol.50 , pp. 284-316
    • Post, E.L.1
  • 60
    • 0001551696 scopus 로고
    • Interpolation and embedding in the recursively enumerable degrees
    • Robinson R.W. Interpolation and embedding in the recursively enumerable degrees. Ann. of Math. 93 2 (1971) 285-314
    • (1971) Ann. of Math. , vol.93 , Issue.2 , pp. 285-314
    • Robinson, R.W.1
  • 63
    • 0003319386 scopus 로고
    • Degrees of Unsolvability
    • Princeton University Press, Princeton, NJ
    • Sacks G.E. Degrees of Unsolvability. Ann. of Math. Stud. Vol. 55 (1963), Princeton University Press, Princeton, NJ
    • (1963) Ann. of Math. Stud. , vol.55
    • Sacks, G.E.1
  • 64
    • 0000152941 scopus 로고
    • Recursive enumerability and the jump operator
    • Sacks G.E. Recursive enumerability and the jump operator. Trans. Amer. Math. Soc. 108 (1963) 223-239
    • (1963) Trans. Amer. Math. Soc. , vol.108 , pp. 223-239
    • Sacks, G.E.1
  • 65
    • 0001503316 scopus 로고
    • On the degrees less than O′
    • Sacks G.E. On the degrees less than O′. Ann. of Math. 77 2 (1963) 211-231
    • (1963) Ann. of Math. , vol.77 , Issue.2 , pp. 211-231
    • Sacks, G.E.1
  • 66
    • 0000121506 scopus 로고
    • The recursively enumerable degrees are dense
    • Sacks G.E. The recursively enumerable degrees are dense. Ann. of Math. 80 2 (1964) 300-312
    • (1964) Ann. of Math. , vol.80 , Issue.2 , pp. 300-312
    • Sacks, G.E.1
  • 67
    • 0007391896 scopus 로고
    • Degrees of Unsolvability
    • Princeton University Press, Princeton, NJ
    • Sacks G.E. Degrees of Unsolvability. Ann. of Math. Stud. 2nd ed. Vol. 55 (1966), Princeton University Press, Princeton, NJ
    • (1966) Ann. of Math. Stud. 2nd ed. , vol.55
    • Sacks, G.E.1
  • 68
    • 0001676326 scopus 로고
    • On degrees of unsolvability
    • Shoenfield J.R. On degrees of unsolvability. Ann. Math. 69 2 (1959) 644-653
    • (1959) Ann. Math. , vol.69 , Issue.2 , pp. 644-653
    • Shoenfield, J.R.1
  • 69
    • 0010658675 scopus 로고
    • Undecidable and creative theories
    • Shoenfield J.R. Undecidable and creative theories. Fund. Math. 49 (1961) 171-179
    • (1961) Fund. Math. , vol.49 , pp. 171-179
    • Shoenfield, J.R.1
  • 70
    • 0002908280 scopus 로고
    • An application of model theory to degrees of unsolvability
    • Addison J.W., Henkin L., and Tarski A. (Eds), North-Holland, Amsterdam
    • Shoenfield J.R. An application of model theory to degrees of unsolvability. In: Addison J.W., Henkin L., and Tarski A. (Eds). Symposium on the Theory of Models (1965), North-Holland, Amsterdam 359-363
    • (1965) Symposium on the Theory of Models , pp. 359-363
    • Shoenfield, J.R.1
  • 71
    • 0004017465 scopus 로고
    • Degrees of Unsolvability
    • North-Holland, Amsterdam
    • Shoenfield J.R. Degrees of Unsolvability. Math. Stud. Vol. 2 (1971), North-Holland, Amsterdam
    • (1971) Math. Stud. , vol.2
    • Shoenfield, J.R.1
  • 73
    • 77956961922 scopus 로고
    • On the ∀∃-sentences of α-recursion theory
    • Generalized Recursion Theory II. Fenstad J.E., Gandy R.O., and Sacks G.E. (Eds), North-Holland, Amsterdam
    • Shore R.A. On the ∀∃-sentences of α-recursion theory. In: Fenstad J.E., Gandy R.O., and Sacks G.E. (Eds). Generalized Recursion Theory II. Studies in Logic and the Foundations of Mathematics Vol. 94 (1978), North-Holland, Amsterdam 331-354
    • (1978) Studies in Logic and the Foundations of Mathematics , vol.94 , pp. 331-354
    • Shore, R.A.1
  • 74
    • 0000256858 scopus 로고
    • Finitely generated codings and the degrees r.e. in a degree d
    • Shore R.A. Finitely generated codings and the degrees r.e. in a degree d. Proc. Amer. Math. Soc. 84 (1982) 256-263
    • (1982) Proc. Amer. Math. Soc. , vol.84 , pp. 256-263
    • Shore, R.A.1
  • 75
    • 38249029246 scopus 로고
    • A non-inversion theorem for the jump operator
    • Shore R.A. A non-inversion theorem for the jump operator. Ann. Pure Appl. Logic 40 (1988) 277-303
    • (1988) Ann. Pure Appl. Logic , vol.40 , pp. 277-303
    • Shore, R.A.1
  • 77
    • 0001636778 scopus 로고
    • Working below a high recursively enumerable degree
    • Shore R.A., and Slaman T.A. Working below a high recursively enumerable degree. J. Symbolic Logic 58 (1993) 824-859
    • (1993) J. Symbolic Logic , vol.58 , pp. 824-859
    • Shore, R.A.1    Slaman, T.A.2
  • 78
    • 0003138259 scopus 로고
    • Degree structures
    • Kyoto 1990, Springer, Tokyo
    • Slaman T.A. Degree structures. Proc. Int. Cong. Math. Kyoto 1990 (1991), Springer, Tokyo 303-316
    • (1991) Proc. Int. Cong. Math. , pp. 303-316
    • Slaman, T.A.1
  • 79
    • 0040660626 scopus 로고
    • The density of infima in the recursively enumerable degrees
    • Slaman T.A. The density of infima in the recursively enumerable degrees. Ann Pure Appl. Logic 52 (1991) 155-179
    • (1991) Ann Pure Appl. Logic , vol.52 , pp. 155-179
    • Slaman, T.A.1
  • 80
    • 77956962080 scopus 로고    scopus 로고
    • The global Turing degrees
    • Griffor E.R. (Ed), Elsevier, Amsterdam
    • Slaman T.A. The global Turing degrees. In: Griffor E.R. (Ed). Handbook of Computability Theory (1999), Elsevier, Amsterdam 155-168
    • (1999) Handbook of Computability Theory , pp. 155-168
    • Slaman, T.A.1
  • 81
    • 0028814031 scopus 로고
    • Algebraic aspects of the computably enumerable degrees
    • Slaman T.A., and Soare R.I. Algebraic aspects of the computably enumerable degrees. Proc. Nat. Acad. Sci. 92 (1995) 617-621
    • (1995) Proc. Nat. Acad. Sci. , vol.92 , pp. 617-621
    • Slaman, T.A.1    Soare, R.I.2
  • 82
    • 77956958659 scopus 로고    scopus 로고
    • Extension of embeddings in the recursively enumerable degrees
    • to appear
    • to appear. Slaman T.A., and Soare R.I. Extension of embeddings in the recursively enumerable degrees. Ann. Math. (1998)
    • (1998) Ann. Math.
    • Slaman, T.A.1    Soare, R.I.2
  • 83
    • 0010711917 scopus 로고
    • Definable functions on degrees
    • Cabal Seminar 81-85. Kechris A.S., Martin D.A., and Steel J.R. (Eds), Springer, Berlin
    • Slaman T., and Steel J.R. Definable functions on degrees. In: Kechris A.S., Martin D.A., and Steel J.R. (Eds). Cabal Seminar 81-85. Lecture Notes in Mathematics Vol. 1333 (1988), Springer, Berlin 37-55
    • (1988) Lecture Notes in Mathematics , vol.1333 , pp. 37-55
    • Slaman, T.1    Steel, J.R.2
  • 86
    • 77956949434 scopus 로고    scopus 로고
    • The lattice of recursively enumerable sets
    • Soare R.I. The lattice of recursively enumerable sets. this Handbook (1999)
    • (1999) this Handbook
    • Soare, R.I.1
  • 87
    • 0000541499 scopus 로고
    • A classification of jump operators
    • Steel J.R. A classification of jump operators. J. Symbolic Logic 47 (1982) 347-358
    • (1982) J. Symbolic Logic , vol.47 , pp. 347-358
    • Steel, J.R.1
  • 88
    • 84960561455 scopus 로고
    • On computable numbers, with an application to the Entscheidungsproblem
    • Turing A.M. On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. 42 2 (1936) 230-265
    • (1936) Proc. London Math. Soc. , vol.42 , Issue.2 , pp. 230-265
    • Turing, A.M.1
  • 89
    • 84960599352 scopus 로고
    • Systems of logic based on ordinals
    • Turing A.M. Systems of logic based on ordinals. Proc. London Math. Soc. 45 (1939) 161-228
    • (1939) Proc. London Math. Soc. , vol.45 , pp. 161-228
    • Turing, A.M.1
  • 90
    • 0003997331 scopus 로고
    • On Embeddings of the 1-3-1 into the Recursively Enumerable Degrees
    • University of California, Berkeley
    • Weinstein B.J. On Embeddings of the 1-3-1 into the Recursively Enumerable Degrees. PhD Thesis (1988), University of California, Berkeley
    • (1988) PhD Thesis
    • Weinstein, B.J.1
  • 91
    • 84972525203 scopus 로고
    • Three theorems on the degrees of recursively enumerable sets
    • Yates C.E.M. Three theorems on the degrees of recursively enumerable sets. Duke Math. J. 32 (1965) 461-468
    • (1965) Duke Math. J. , vol.32 , pp. 461-468
    • Yates, C.E.M.1
  • 92
    • 0000288556 scopus 로고
    • A minimal pair of recursively enumerable degrees
    • Yates C.E.M. A minimal pair of recursively enumerable degrees. J. Symbolic Logic 31 (1966) 159-168
    • (1966) J. Symbolic Logic , vol.31 , pp. 159-168
    • Yates, C.E.M.1
  • 93
    • 0010709062 scopus 로고
    • On the degrees of index sets
    • Yates C.E.M. On the degrees of index sets. Trans. Amer. Math. Soc. 121 (1966) 309-328
    • (1966) Trans. Amer. Math. Soc. , vol.121 , pp. 309-328
    • Yates, C.E.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.