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Manuel Lerman [30]M. Lerman [17]Mannel Lerman [1]
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  1. On a Conjecture of Dobrinen and Simpson Concerning Almost Everywhere Domination.Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman & Reed Solomon - 2006 - Journal of Symbolic Logic 71 (1):119 - 136.
  2.  6
    Separating Principles Below Ramsey's Theorem for Pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
    In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.
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  3.  5
    Degrees of Unsolvability: Local and Global Theory.M. Lerman - 1983 - Springer Verlag.
  4. 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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  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.  27
    Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion.C. G. Jockusch, M. Lerman, R. I. Soare & R. M. Solovay - 1989 - Journal of Symbolic Logic 54 (4):1288-1323.
  7.  2
    [Omnibus Review].M. Lerman - 1985 - Journal of Symbolic Logic 50 (2):550-552.
  8.  12
    A Necessary and Sufficient Condition for Embedding Ranked Finite Partial Lattices Into the Computably Enumerable Degrees.M. Lerman - 1998 - Annals of Pure and Applied Logic 94 (1-3):143-180.
    We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.
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  9.  25
    Lattice Embeddings Into the Recursively Enumerable Degrees.K. Ambos-Spies & M. Lerman - 1986 - Journal of Symbolic Logic 51 (2):257-272.
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  10.  6
    Degrees Which Do Not Bound Minimal Degrees.Manuel Lerman - 1986 - Annals of Pure and Applied Logic 30 (3):249-276.
  11.  9
    A Necessary and Sufficient Condition for Embedding Principally Decomposable Finite Lattices Into the Computably Enumerable Degrees.M. Lerman - 2000 - Annals of Pure and Applied Logic 101 (2-3):275-297.
    We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.
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  12.  15
    Upper Bounds for the Arithmetical Degrees.M. Lerman - 1983 - Annals of Pure and Applied Logic 29 (3):225-254.
  13.  12
    Lattice Embeddings Into the Recursively Enumerable Degrees. II.K. Ambos-Spies & M. Lerman - 1989 - Journal of Symbolic Logic 54 (3):735-760.
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  14.  20
    Self-Embeddings of Computable Trees.Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, James H. Schmerl & Reed Solomon - 2008 - Notre Dame Journal of Formal Logic 49 (1):1-37.
    We divide the class of infinite computable trees into three types. For the first and second types, 0' computes a nontrivial self-embedding while for the third type 0'' computes a nontrivial self-embedding. These results are optimal and we obtain partial results concerning the complexity of nontrivial self-embeddings of infinite computable trees considered up to isomorphism. We show that every infinite computable tree must have either an infinite computable chain or an infinite Π01 antichain. This result is optimal and has connections (...)
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  15.  20
    Carl G. JockuschJr., and David B. Posner. Double Jumps of Minimal Degrees. The Journal of Symbolic Logic, Vol. 43 No. 4 , Pp. 715–724. - Carl G. JockuschJr., and David B. Posner. Automorphism Bases for Degrees of Unsotvability. Israel Journal of Mathematics, Vol. 40 , Pp. 150–164. - Richard L. Epstein. Initial Segments of Degrees Below 0′. Memoirs of the American Mathematical Society, No. 241. American Mathematical Society, Providence1981, Vi + 102 Pp. - Richard A. Shore. The Theory of the Degrees Below 0′. The Journal of the London Mathematical Society, Ser. 2 Vol. 24 , Pp. 1–14.M. Lerman - 1985 - Journal of Symbolic Logic 50 (2):550-552.
  16.  10
    Hyperhypersimple α-r.e. sets.C. T. Chong & M. Lerman - 1976 - Annals of Mathematical Logic 9 (1-2):1-48.
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  17.  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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  18.  52
    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. Some Theorems on R-Maximal Sets and Major Subsets of Recursively Enumerable Sets.Manuel Lerman - 1971 - Journal of Symbolic Logic 36 (2):193-215.
  20.  7
    The Universal Splitting Property. II.M. Lerman & J. B. Remmel - 1984 - Journal of Symbolic Logic 49 (1):137-150.
  21.  9
    Admissible Ordinals and Priority Arguments.Manuel Lerman - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 311--344.
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  22.  24
    Ideals of Generalized Finite Sets in Lattices of Α-Recursively Enumerable Sets.Manuel Lerman - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):347-352.
  23.  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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  24.  33
    Least Upper Bounds for Minimal Pairs of Α-R.E. Α-Degrees.Manuel Lerman - 1974 - Journal of Symbolic Logic 39 (1):49-56.
  25.  11
    Types of Simple Α-Recursively Enumerable Sets.Manuel Lerman - 1976 - Journal of Symbolic Logic 41 (2):419-426.
  26.  8
    Ideals of Generalized Finite Sets in Lattices of Α‐Recursively Enumerable Sets.Manuel Lerman - 1976 - Mathematical Logic Quarterly 22 (1):347-352.
  27.  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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  28.  17
    Theories with Recursive Models.Manuel Lerman & James H. Schmerl - 1979 - Journal of Symbolic Logic 44 (1):59-76.
  29.  12
    Congruence Relations, Filters, Ideals, and Definability in Lattices of Α-Recursively Enumerable Sets.Manuel Lerman - 1976 - Journal of Symbolic Logic 41 (2):405-418.
  30.  23
    Minimal Degrees and Recursively Inseparable Pairs of Recursively Enumerable Sets.Manuel Lerman - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (19-22):331-342.
  31.  5
    R. PETER [1934] Uber den Zussammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann.Sc Kleene, El Post, M. Kline, M. Lerman, L. Lowenheim, D. Normann, P. Odifreddi, G. Peano, Cs Peirce & R. Penrose - 1999 - In Edward R. Griffor (ed.), Handbook of Computability Theory. Elsevier. pp. 34.
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  32.  14
    Some Nondistributive Lattices as Initial Segments of the Degrees of Unsolvability.Manuel Lerman - 1969 - Journal of Symbolic Logic 34 (1):85-98.
  33.  21
    Turing Degrees and Many-One Degrees of Maximal Sets.Manuel Lerman - 1970 - Journal of Symbolic Logic 35 (1):29-40.
  34.  11
    Minimal Degrees and Recursively Inseparable Pairs of Recursively Enumerable Sets.Manuel Lerman - 1991 - Mathematical Logic Quarterly 37 (19‐22):331-342.
  35.  12
    Computable Choice Functions for Computable Linear Orderings.Manuel Lerman & Richard Watnick - 2003 - Mathematical Logic Quarterly 49 (5):485-510.
    A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of order-types, each of (...)
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  36.  11
    Embedding Finite Lattices Into the Ideals of Computably Enumerable Turing Degrees.William C. Calhoun & Manuel Lerman - 2001 - Journal of Symbolic Logic 66 (4):1791-1802.
    We show that the lattice L 20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (J). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π 2 necessary and sufficient condition for embedding a finite pseudolattice into J.
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  37.  6
    Homomorphisms and Quotients of Degree Structures.Burkhard Englert, Manuel Lerman & Kevin Wald - 2003 - Annals of Pure and Applied Logic 123 (1-3):193-233.
    We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.
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  38. Griffor, ER, See Rathjen, M.L. Harrington, R. I. Soare, J. F. Knight & M. Lerman - 1998 - Annals of Pure and Applied Logic 94:297.
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  39.  14
    A Framework for Priority Arguments.M. Lerman - 2010 - Cambridge University Press.
    This book presents a unifying framework for using priority arguments to prove theorems in computability.
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  40. Logic Year 1979-80, the University of Connecticut, Usa.M. Lerman, J. H. Schmerl & R. I. Soare (eds.) - 1981 - Springer Verlag.