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Intervals without Critical Triples

Published online by Cambridge University Press:  24 March 2017

P. Cholak
Affiliation:
University of Notre Dame
R. Downey
Affiliation:
Department of Mathematics Victoria University of Wellington
R. Shore
Affiliation:
Department of Mathematics White Hall, Cornell University Ithaca
Johann A. Makowsky
Affiliation:
Technion - Israel Institute of Technology, Haifa
Elena V. Ravve
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Publisher: Cambridge University Press
Print publication year: 2017

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References

[ASF96] Ambos-Spies, K., Fejer, P. A. 1996. Personal communication.
[ASL86] Ambos-Spies, K., Lerman, M. 1986. Lattice embeddings into the recursively enumerable degrees, J. Symbolic Logic 51: 257–272.Google Scholar
[ASL89] Ambos-Spies, K., Lerman, M. 1989. Lattice embeddings into the recursively enumerable degrees II,]. Symbolic Logic 54: 735–759.Google Scholar
[CDo93] Cholak, P., Downey, R. 1993. Lattice nonembeddings and intervals of the recursively enumerable degrees, Ann. Pure Appl. Logic 61: 195–221.Google Scholar
[CYi] Cooper, B., Yi, X. n.d. Non-splitting and the high/low hierarchy. In preparation.
[Dow90] Downey, R. G. 1990. Lattice nonembedding and initial segments of the r. e. degrees, Ann. Pure Appl. Logic 49: 97–119.Google Scholar
[DLe] Downey, R. G., Lempp, S. n.d. Contiguity and distributivity in the computably enumerable turing degrees, J. Symbolic Logic. To appear.
[DSh95] Downey, R. G., Shore, R. A. 1995. Degree theoretic definitions of low2 recursively enumerable sets, J. Symbolic Logic 60(3): 727–756.Google Scholar
[DSh96] Downey, R. G., Shore, R. A. 1996. Lattice embedding below a nonlow2 recursively enumerable degree, Israel J. Math. 94: 221–246.Google Scholar
[JSh83] Jockusch, C. G. Jr., Shore, R. A. 1983. Pseudo-jump operators I: the r.e. case, Trans. Amer. Math. Soc. 275: 599–609.Google Scholar
[Lac72] Lachlan, A. H. 1972. Embedding nondistributive lattices in the recursively enumerable degrees, in Hodges, W. (ed.), Conference in Mathematical Logic, London, 1970, Vol. 255 of Lecture Notes in Mathematics, Springer-Verlag, Heidelberg, pp. 149–177.
[LS08O] Lachlan, A. H., Soare, R. I. 1980. Not every finite lattice is embeddable in the recursively enumerable degrees, Adv. in Math. 37: 74–82.Google Scholar
[LLe] Lempp, S., Lerman, M. n.d. A finite lattice without a critical triple that cannot be embedded into the enumerable turing degree, Ann. Pure Appl. Logic. To appear.
[Leoi 1994] Leonhardi, S. 1994. Generalized Nonsplitting in the Recursively Enumerable Degrees, PhD thesis, University of Wisconsin.
[NSS] Nies, A., Shore, R. A., Slaman, T. A. n.d. Definability in the recursively enumerable degrees. In preparation.
[Sho] Shore, R. A. n.d. The recursively enumerable degrees, in Griffor, E. (ed.), The Handbook of Recursion Theory, North-Holland. To appear.
[SS191] Shore, R. A., Slaman, T. A. 1991. Working below a low2 recursively enumerable degree, Ann. Pure Appl. Logic 52: 1–25.Google Scholar
[Soa87] Soare, R. I. 1987. Recursively Enumerable Sets and Degrees, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Heidelberg.
[Wei88] Weinstein, B. 1988. On Embedding of the Lattice 1-3-1 into the Recursively Enumerable Degrees, PhD thesis, University of California, Berkeley.

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  • Intervals without Critical Triples
    • By P. Cholak, University of Notre Dame, R. Downey, Department of Mathematics Victoria University of Wellington, R. Shore, Department of Mathematics White Hall, Cornell University Ithaca
  • Edited by Johann A. Makowsky, Technion - Israel Institute of Technology, Haifa, Elena V. Ravve, Technion - Israel Institute of Technology, Haifa
  • Book: Logic Colloquium '95
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316716830.005
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  • Intervals without Critical Triples
    • By P. Cholak, University of Notre Dame, R. Downey, Department of Mathematics Victoria University of Wellington, R. Shore, Department of Mathematics White Hall, Cornell University Ithaca
  • Edited by Johann A. Makowsky, Technion - Israel Institute of Technology, Haifa, Elena V. Ravve, Technion - Israel Institute of Technology, Haifa
  • Book: Logic Colloquium '95
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316716830.005
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.

  • Intervals without Critical Triples
    • By P. Cholak, University of Notre Dame, R. Downey, Department of Mathematics Victoria University of Wellington, R. Shore, Department of Mathematics White Hall, Cornell University Ithaca
  • Edited by Johann A. Makowsky, Technion - Israel Institute of Technology, Haifa, Elena V. Ravve, Technion - Israel Institute of Technology, Haifa
  • Book: Logic Colloquium '95
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316716830.005
Available formats
×