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Steffen Lempp [63]S. Lempp [5]
  1.  37
    The D.R.E. Degrees Are Not Dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  2.  21
    Universal Computably Enumerable Equivalence Relations.Uri Andrews, Steffen Lempp, Joseph S. Miller, Keng Meng Ng, Luca San Mauro & Andrea Sorbi - 2014 - Journal of Symbolic Logic 79 (1):60-88.
  3.  22
    The D.R.E. Degrees Are Not Dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  4.  36
    A Δ20 Set with No Infinite Low Subset in Either It or its Complement.Rod Downey, Denis R. Hirschfeldt, Steffen Lempp & Reed Solomon - 2001 - Journal of Symbolic Logic 66 (3):1371-1381.
    We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every ω-model of RCA 0 + SRT 2 2 must contain a nonlow set.
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  5.  16
    A Finite Lattice Without Critical Triple That Cannot Be Embedded Into the Enumerable Turing Degrees.Steffen Lempp & Manuel Lerman - 1997 - Annals of Pure and Applied Logic 87 (2):167-185.
    We exhibit a finite lattice without critical triple that cannot be embedded into the enumerable Turing degrees. Our method promises to lead to a full characterization of the finite lattices embeddable into the enumerable Turing degrees.
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  6.  30
    Highness and Bounding Minimal Pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.
  7. On Extensions of Embeddings Into the Enumeration Degrees of the -Sets.Steffen Lempp, Theodore A. Slaman & Andrea Sorbi - 2005 - Journal of Mathematical Logic 5 (02):247-298.
    We give an algorithm for deciding whether an embedding of a finite partial order [Formula: see text] into the enumeration degrees of the [Formula: see text]-sets can always be extended to an embedding of a finite partial order [Formula: see text].
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  8.  26
    Computable Categoricity of Trees of Finite Height.Steffen Lempp, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Journal of Symbolic Logic 70 (1):151-215.
    We characterize the structure of computably categorical trees of finite height, and prove that our criterion is both necessary and sufficient. Intuitively, the characterization is easiest to express in terms of isomorphisms of (possibly infinite) trees, but in fact it is equivalent to a Σ03-condition. We show that all trees which are not computably categorical have computable dimension ω. Finally, we prove that for every n≥ 1 in ω, there exists a computable tree of finite height which is δ0n+1-categorical but (...)
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  9.  32
    Comparing DNR and WWKL.Klaus Ambos-Spies, Bjørn Kjos-Hanssen, Steffen Lempp & Theodore A. Slaman - 2004 - Journal of Symbolic Logic 69 (4):1089-1104.
    In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0.
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  10. Stability and Posets.Carl Jockusch Jr, Bart Kastermans, Steffen Lempp, Manuel Lerman & Reed Solomon - 2009 - Journal of Symbolic Logic 74 (2):693 - 711.
    Hirschfeldt and Shore have introduced a notion of stability for infinite posets. We define an arguably more natural notion called weak stability, and we study the existence of infinite computable or low chains or antichains, and of infinite $\Pi _1^0 $ chains and antichains, in infinite computable stable and weakly stable posets. For example, we extend a result of Hirschfeldt and Shore to show that every infinite computable weakly stable poset contains either an infinite low chain or an infinite computable (...)
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  11.  49
    On Computable Self-Embeddings of Computable Linear Orderings.Rodney G. Downey, Bart Kastermans & Steffen Lempp - 2009 - Journal of Symbolic Logic 74 (4):1352 - 1366.
    We solve a longstanding question of Rosenstein, and make progress toward solving a longstanding open problem in the area of computable linear orderings by showing that every computable ƞ-like linear ordering without an infinite strongly ƞ-like interval has a computable copy without nontrivial computable self-embedding. The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.
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  12.  23
    Filters on Computable Posets.Steffen Lempp & Carl Mummert - 2006 - Notre Dame Journal of Formal Logic 47 (4):479-485.
    We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle (...)
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  13.  42
    On the Existence of a Strong Minimal Pair.George Barmpalias, Mingzhong Cai, Steffen Lempp & Theodore A. Slaman - 2015 - Journal of Mathematical Logic 15 (1):1550003.
    We show that there is a strong minimal pair in the computably enumerable Turing degrees, i.e. a pair of nonzero c.e. degrees a and b such that a∩b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.
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  14.  31
    On the Complexity of the Successivity Relation in Computable Linear Orderings.Rod Downey, Steffen Lempp & Guohua Wu - 2010 - Journal of Mathematical Logic 10 (1):83-99.
    In this paper, we solve a long-standing open question, about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of (...)
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  15.  42
    The Undecidability of the II4 Theory for the R. E. Wtt and Turing Degrees.Steffen Lempp & André Nies - 1995 - Journal of Symbolic Logic 60 (4):1118 - 1136.
    We show that the Π 4 -theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.
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  16.  48
    A General Framework for Priority Arguments.Steffen Lempp & Manuel Lerman - 1995 - Bulletin of Symbolic Logic 1 (2):189-201.
    The degrees of unsolvability were introduced in the ground-breaking papers of Post [20] and Kleene and Post [7] as an attempt to measure theinformation contentof sets of natural numbers. Kleene and Post were interested in the relative complexity of decision problems arising naturally in mathematics; in particular, they wished to know when a solution to one decision problem contained the information necessary to solve a second decision problem. As decision problems can be coded by sets of natural numbers, this question (...)
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  17.  38
    The Undecidability of the II$^_4$ Theory for the R. E. Wtt and Turing Degrees.Steffen Lempp & André Nies - 1995 - Journal of Symbolic Logic 60 (4):1118-1136.
    We show that the $\Pi_4$-theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.
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  18.  53
    Decidability of the Two-Quantifier Theory of the Recursively Enumerable Weak Truth-Table Degrees and Other Distributive Upper Semi-Lattices.Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp & Manuel Lerman - 1996 - Journal of Symbolic Logic 61 (3):880-905.
    We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...)
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  19.  23
    A Limit on Relative Genericity in the Recursively Enumerable Sets.Steffen Lempp & Theodore A. Slaman - 1989 - Journal of Symbolic Logic 54 (2):376-395.
    Work in the setting of the recursively enumerable sets and their Turing degrees. A set X is low if X', its Turning jump, is recursive in $\varnothing'$ and high if X' computes $\varnothing''$ . Attempting to find a property between being low and being recursive, Bickford and Mills produced the following definition. W is deep, if for each recursively enumerable set A, the jump of $A \bigoplus W$ is recursive in the jump of A. We prove that there are no (...)
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  20.  6
    Bezem, M., see Barendsen, E.G. M. Bierman, M. DZamonja, S. Shelah, S. Feferman, G. Jiiger, M. A. Jahn, S. Lempp, Sui Yuefei, S. D. Leonhardi & D. Macpherson - 1996 - Annals of Pure and Applied Logic 79 (1):317.
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  21.  17
    Lowness for Effective Hausdorff Dimension.Steffen Lempp, Joseph S. Miller, Keng Meng Ng, Daniel D. Turetsky & Rebecca Weber - 2014 - Journal of Mathematical Logic 14 (2):1450011.
    We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...)
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  22.  28
    Jumps of Nontrivial Splittings of Recursively Enumerable Sets.Michael A. Ingrassia & Steffen Lempp - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (4):285-292.
  23.  33
    Jumps of Nontrivial Splittings of Recursively Enumerable Sets.Michael A. Ingrassia & Steffen Lempp - 1990 - Mathematical Logic Quarterly 36 (4):285-292.
  24.  29
    The Existential Theory of the Poset of R.E. Degrees with a Predicate for Single Jump Reducibility.Steffen Lempp & Manuel Lerman - 1992 - Journal of Symbolic Logic 57 (3):1120-1130.
    We show the decidability of the existential theory of the recursively enumerable degrees in the language of Turing reducibility, Turing reducibility of the Turing jumps, and least and greatest element.
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  25.  57
    A Decomposition of the Rogers Semilattice of a Family of D.C.E. Sets.Serikzhan A. Badaev & Steffen Lempp - 2009 - Journal of Symbolic Logic 74 (2):618-640.
    Khutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. sets, has (up (...)
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  26.  1
    Archangel&y, DA, Dekhtyar, MI and Taitslin, MA, Linear Logic For.M. A. Arslanov, S. Lempp, R. A. Shore, S. Artemov, V. Krupski, A. Dabrowski, L. S. Moss, R. Parikh, T. Eiter & G. Gottlob - 1996 - Annals of Pure and Applied Logic 78 (1-3):271.
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  27. On the Filter of Computably Enumerable Supersets of an R-Maximal Set.Steffen Lempp, André Nies & D. Reed Solomon - 2001 - Archive for Mathematical Logic 40 (6):415-423.
    We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
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  28.  34
    Iterated Trees of Strategies and Priority Arguments.Steffen Lempp & Manuel Lerman - 1997 - Archive for Mathematical Logic 36 (4-5):297-312.
    . We describe the motivation for the construction of a general framework for priority arguments, the ideas incorporated into the construction of the framework, and the use of the framework to prove theorems in computability theory which require priority arguments.
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  29.  26
    Interpolating D-R.E. And REA Degrees Between R.E. Degrees.Marat Arslanov, Steffen Lempp & Richard A. Shore - 1996 - Annals of Pure and Applied Logic 78 (1-3):29-56.
    We provide three new results about interpolating 2-r.e. or 2-REA degrees between given r.e. degrees: Proposition 1.13. If c h are r.e. , c is low and h is high, then there is an a h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h g there is a properly d-r.e. degree a such that h a g and a is r.e. in h . Theorem 3.1. There is an incomplete nonrecursive r.e. A (...)
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  30.  2
    On Downey's Conjecture.Marat M. Arslanov, Iskander Sh Kalimullin & Steffen Lempp - 2010 - Journal of Symbolic Logic 75 (2):401-441.
    We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.
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  31.  16
    Infinite Versions of Some Problems From Finite Complexity Theory.Jeffry L. Hirst & Steffen Lempp - 1996 - Notre Dame Journal of Formal Logic 37 (4):545-553.
    Recently, several authors have explored the connections between NP-complete problems for finite objects and the complexity of their analogs for infinite objects. In this paper, we will categorize infinite versions of several problems arising from finite complexity theory in terms of their recursion theoretic complexity and proof theoretic strength. These infinite analogs can behave in a variety of unexpected ways.
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  32.  37
    Contiguity and Distributivity in the Enumerable Turing Degrees.Rodney G. Downey & Steffen Lempp - 1997 - Journal of Symbolic Logic 62 (4):1215-1240.
    We prove that a enumerable degree is contiguous iff it is locally distributive. This settles a twenty-year old question going back to Ladner and Sasso. We also prove that strong contiguity and contiguity coincide, settling a question of the first author, and prove that no $m$-topped degree is contiguous, settling a question of the first author and Carl Jockusch [11]. Finally, we prove some results concerning local distributivity and relativized weak truth table reducibility.
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  33. Master Index to Volumes 71-80.K. A. Abrahamson, R. G. Downey, M. R. Fellows, A. W. Apter, M. Magidor, M. I. da ArchangelskyDekhtyar, M. A. Taitslin, M. A. Arslanov & S. Lempp - 1996 - Annals of Pure and Applied Logic 80:293-298.
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  34.  3
    Computability and the Symmetric Difference Operator.Uri Andrews, Peter M. Gerdes, Steffen Lempp, Joseph S. Miller & Noah D. Schweber - forthcoming - Logic Journal of the IGPL.
    Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.
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  35. Recursion Theory and Complexity: Proceedings of the Kazan '97 Workshop, Kazan, Russia, July 14-19, 1997.M. M. Arslanov & Steffen Lempp (eds.) - 1999 - W. De Gruyter.
    This volume contains papers from the recursion theory session of the Kazan Workshop on Recursion and Complexity Theory. Recursion theory, the study of computability, is an area of mathematical logic that has traditionally been particularly strong in the United States and the former Soviet Union. This was the first workshop ever to bring together about 50 international experts in recursion theory from the United States, the former Soviet Union and Western Europe.
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  36.  7
    Corrigendum to “The D.R.E. Degrees Are Not Dense” [Ann. Pure Appl. Logic 55 (1991) 125–151].S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 2017 - Annals of Pure and Applied Logic 168 (12):2164-2165.
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  37.  19
    Conference on Computability, Complexity and Randomness.Verónica Becher, C. T. Chong, Rod Downey, Noam Greenberg, Antonin Kucera, Bjørn Kjos-Hanssen, Steffen Lempp, Antonio Montalbán, Jan Reimann & Stephen Simpson - 2008 - Bulletin of Symbolic Logic 14 (4):548-549.
  38.  24
    Copies of Books to Asl, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference. [REVIEW]Anuj Dawar Colyvan, Steffen Lempp, Rahim Moosa, Ernest Schimmerling & Alex Simpson - 2013 - Bulletin of Symbolic Logic 19 (2).
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  39.  5
    A $Delta^02$ Set with Barely $Sigma^02$ Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700-1718.
    We construct a $\Delta^0_2$ degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.
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  40.  20
    A Δ02 Set with Barely Σ02 Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700 - 1718.
    We construct a Δ 0 2 degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.
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  41.  4
    A Set with Barely Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700-1718.
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  42.  37
    Corrigendum: ``Contiguity and Distributivity in the Enumerable Turing Degrees''.Rodney G. Downey & Steffen Lempp - 2002 - Journal of Symbolic Logic 67 (4):1579-1580.
  43.  34
    Corrigendum: "On the Complexity of the Successivity Relation in Computable Linear Orderings".Rodney G. Downey, Steffen Lempp & Guohua Wu - 2017 - Journal of Mathematical Logic 17 (2):1792002.
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  44.  28
    There is No Plus-Capping Degree.Rodney G. Downey & Steffen Lempp - 1994 - Archive for Mathematical Logic 33 (2):109-119.
    Answering a question of Per Lindström, we show that there is no “plus-capping” degree, i.e. that for any incomplete r.e. degreew, there is an incomplete r.e. degreea>w such that there is no r.e. degreev>w witha∩v=w.
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  45.  12
    Phoenix Civic Plaza, Phoenix, Arizona, January 9–10, 2004.Matthew Foreman, Steve Jackson, Julia Knight, R. W. Knight, Steffen Lempp, Françoise Point, Kobi Peterzil, Leonard Schulman, Slawomir Solecki & Carol Wood - 2004 - Bulletin of Symbolic Logic 10 (2).
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  46.  2
    Computable Linear Orders and Products.Andrey N. Frolov, Steffen Lempp, Keng Meng Ng & Guohua Wu - 2020 - Journal of Symbolic Logic 85 (2):605-623.
    We characterize the linear order types $\tau $ with the property that given any countable linear order $\mathcal {L}$, $\tau \cdot \mathcal {L}$ is a computable linear order iff $\mathcal {L}$ is a computable linear order, as exactly the finite nonempty order types.
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  47.  13
    Computability and Uncountable Linear Orders I: Computable Categoricity.Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky - 2015 - Journal of Symbolic Logic 80 (1):116-144.
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  48.  15
    Computability and Uncountable Linear Orders II: Degree Spectra.Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky - 2015 - Journal of Symbolic Logic 80 (1):145-178.
  49.  8
    Reductions Between Types of Numberings.Ian Herbert, Sanjay Jain, Steffen Lempp, Manat Mustafa & Frank Stephan - 2019 - Annals of Pure and Applied Logic 170 (12):102716.
    This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the k+1-r.e. numberings; all further reductions are obtained by (...)
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  50.  9
    University of California, San Diego, March 20–23, 1999.Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (3).
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