55 found
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  1.  18
    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.
  2.  32
    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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  3. 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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  4.  32
    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. 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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  6.  18
    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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  7.  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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  8.  45
    Embedding Finite Lattices Into the Σ20 Enumeration Degrees.Steffen Lempp & Andrea Sorbi - 2002 - Journal of Symbolic Logic 67 (1):69-90.
    We show that every finite lattice is embeddable into the Σ 0 2 enumeration degrees via a lattice-theoretic embedding which preserves 0 and 1.
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  9.  41
    Heinz-Dieter Ebbinghaus, Jörg Flum, and Wolfgang Thomas. Einführung in Die Mathematische Logik. Die Mathematik. Wissenschaftliche Buchgesellschaft, Darmstadt1978, Ix + 288 Pp. - H.-D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic. Revised English Translation by Ann S. Ferebee of the Preceding. Undergraduate Texts in Mathematics. Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1984, Ix + 216 Pp. - Heinz-Dieter Ebbinghaus, Jörg Flum, and Wolfgang Thomas. Einführung in Die Mathematische Logik. Second Edition. Die Mathematik. Wissenschaftliche Buchgesellschaft, Darmstadt1986, Ix + 308 Pp. - H.-D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic. Second Edition. Revised English Translation by Ann S. Ferebee and Margit Meßmer of the Preceding. Undergraduate Texts in Mathematics. Springer-Verlag, New York, Berlin, Heidelberg, Etc., 1994, X + 289 Pp. [REVIEW]Steffen Lempp - 1995 - Journal of Symbolic Logic 60 (3):1013-1014.
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  10. 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).
    No categories
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  11.  29
    Highness and Bounding Minimal Pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.
  12.  24
    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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  13.  30
    Ulrich Felgner. Das Induktions-Prinzip. Jahresbericht der Deutschen Mathematiker-Vereinigung. vol. 114, no. 1 , pp. 23–45. - Ulrich Felgner. Hilbert’s “Grundlagen der Geometrie” und ihre Stellung in der Geschichte der Grundlagendiskussion. Jahresbericht der Deutschen Mathematiker-Vereinigung. vol. 115, no. 3-4 , pp. 185–206. [REVIEW]Steffen Lempp - 2014 - Bulletin of Symbolic Logic 20 (2):201-202.
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  14.  40
    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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  15.  23
    Joseph R. Shoenfield. Recursion Theory, Lecture Notes in Logic, No. 1. Springer-Verlag, Berlin, Heidelberg, New York, Etc., 1993, V + 84 Pp. [REVIEW]Steffen Lempp - 1994 - Journal of Symbolic Logic 59 (3):1105.
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  16.  28
    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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  17.  16
    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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  18.  39
    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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  19.  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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  20.  35
    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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  21.  48
    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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  22.  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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  23.  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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  24.  49
    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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  25.  22
    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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  26.  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.
  27.  35
    Kenneth Kunen, The Foundations of Mathematics, Studies in Logic, Mathematical Logic and Foundations, Vol. 19. College Publications, London, 2009, Vii + 251 Pp. [REVIEW]Steffen Lempp - 2016 - Bulletin of Symbolic Logic 22 (2):287-288.
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  28.  32
    Jumps of Nontrivial Splittings of Recursively Enumerable Sets.Michael A. Ingrassia & Steffen Lempp - 1990 - Mathematical Logic Quarterly 36 (4):285-292.
  29.  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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  30.  6
    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.
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  31.  26
    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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  32.  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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  33.  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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  34.  37
    Winter Meeting of the Association for Symbolic Logic: San Antonio, 1993.Steffen Lempp - 1994 - Journal of Symbolic Logic 59 (2):720-729.
  35.  49
    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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  36.  15
    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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  37.  28
    Infima in the Recursively Enumerable Weak Truth Table Degrees.Rich Blaylock, Rod Downey & Steffen Lempp - 1997 - Notre Dame Journal of Formal Logic 38 (3):406-418.
    We show that for every nontrivial r.e. wtt-degree a, there are r.e. wtt-degrees b and c incomparable to a such that the infimum of a and b exists but the infimum of a and c fails to exist. This shows in particular that there are no strongly noncappable r.e. wtt-degrees, in contrast to the situation in the r.e. Turing degrees.
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  38.  25
    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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  39.  21
    The Lindenbaum Algebra of the Theory of the Class of All Finite Models.Steffen Lempp, Mikhail Peretyat'kin & Reed Solomon - 2002 - Journal of Mathematical Logic 2 (02):145-225.
    In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions (...)
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  40.  22
    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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  41.  21
    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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  42.  21
    The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007.Yiannis Moschovakis, Richmond H. Thomason, Steffen Lempp, Steve Awodey, Jean-Pierre Marquis & William Tait - 2007 - Bulletin of Symbolic Logic 13 (4).
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  43.  18
    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.
  44.  11
    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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  45.  11
    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.
  46.  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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  47.  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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  48.  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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  49.  8
    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).
  50.  13
    A High Strongly Noncappable Degree.Steffen Lempp - 1988 - Journal of Symbolic Logic 53 (1):174-187.
    An r.e. degree a ≠ 0, 0' is called strongly noncappable if it has no inf with any incomparable r.e. degree. We show the existence of a high strongly noncappable degree.
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