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Embedding finite lattices into the Σ20 enumeration degrees

  • Steffen Lempp (a1) and Andrea Sorbi (a2)

We show that every finite lattice is embeddable into the Σ20 enumeration degrees via a lattice-theoretic embedding which preserves 0 and 1.

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[4] K. Ambos-Spies , S. Lempp , and M. Lerman , Lattice embeddings into the r. e. degrees preserving 0 and 1, Journal of the London Mathematical Society, vol. 49 (1994), pp. 115.

[8] S. B. Cooper , Enumeration reducibility using bounded information: Counting minimal covers, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 33 (1987), pp. 537560.

[10] A. H. Lachlan , Embedding nondistributive lattices in the recursively enumerable degress, Conference in Mathematical Logic, London, 1970 ( W. Hodges , editor), Lecture Notes in Mathematics, vol. 255, Springer-Verlag, Heidelberg, 1972, pp. 149177.

[11] A. H. Lachlan and R. I Soare , Not every finite lattice is embeddable in the recursively enumerable degrees, Advances in Mathematics, vol. 37 (1980), pp. 7482.

[12] S. Lempp and M. Lerman , A finite lattice without a critical triple that cannot be embedded into the enumerable Turing degrees, Annals of Pure and Applied Logic, vol. 87 (1997), pp. 167185.

[14] A. Nies and A. Sorbi , Branching in the enumeration degrees of Σ20 sets, Israel Journal of Mathematics, vol. 110 (1999), pp. 2959.

[17] R. I. Soare , Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Heidelberg, 1987.

[18] S. K. Thomason , Sublattices of the recursively enumerable degrees, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 17 (1971), pp. 273280.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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