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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ganchev, H. and Soskova, M. 2012. Embedding distributive lattices in the  Formula enumeration degrees. Journal of Logic and Computation, Vol. 22, Issue. 4, p. 779.


    SORBI, ANDREA WU, GUOHUA and YANG, YUE 2010. Diamond embeddings into the enumeration degrees. Mathematical Structures in Computer Science, Vol. 20, Issue. 05, p. 799.


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Embedding finite lattices into the Σ20 enumeration degrees

  • Steffen Lempp (a1) and Andrea Sorbi (a2)
  • DOI: http://dx.doi.org/10.2178/jsl/1190150030
  • Published online: 01 March 2014
Abstract
Abstract

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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