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Manuel Lerman [28]M. Lerman [19]Mannel Lerman [1]
  1. Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman & Reed Solomon (2006). On a Conjecture of Dobrinen and Simpson Concerning Almost Everywhere Domination. Journal of Symbolic Logic 71 (1):119 - 136.
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  2. Carl G. Jockusch, Bart Kastermans, Steffen Lempp, Manuel Lerman & Reed Solomon (2009). Stability and Posets. 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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  3.  2
    M. Lerman (1983). Degrees of Unsolvability: Local and Global Theory. Springer-Verlag.
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  4. Manuel Lerman (1971). Some Theorems on R-Maximal Sets and Major Subsets of Recursively Enumerable Sets. Journal of Symbolic Logic 36 (2):193-215.
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  5. Manuel Lerman, Reed Solomon & Henry Towsner (2013). Separating Principles Below Ramsey's Theorem for Pairs. Journal of Mathematical Logic 13 (2):1350007.
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  6.  7
    C. G. Jockusch Jr, M. Lerman, R. I. Soare & R. M. Solovay (1989). Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion. Journal of Symbolic Logic 54 (4):1288 - 1323.
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  7.  4
    Steffen Lempp & Manuel Lerman (1997). A Finite Lattice Without Critical Triple That Cannot Be Embedded Into the Enumerable Turing Degrees. 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.  3
    M. Lerman (1998). A Necessary and Sufficient Condition for Embedding Ranked Finite Partial Lattices Into the Computably Enumerable Degrees. 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.  9
    K. Ambos-Spies & M. Lerman (1986). Lattice Embeddings Into the Recursively Enumerable Degrees. Journal of Symbolic Logic 51 (2):257-272.
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  10.  6
    M. Lerman (1985). Upper Bounds for the Arithmetical Degrees. Annals of Pure and Applied Logic 29 (3):225-254.
  11.  4
    Manuel Lerman (1976). Ideals of Generalized Finite Sets in Lattices of Α-Recursively Enumerable Sets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):347-352.
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  12.  1
    M. Lerman (2000). A Necessary and Sufficient Condition for Embedding Principally Decomposable Finite Lattices Into the Computably Enumerable Degrees. 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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  13.  4
    Manuel Lerman (1991). Minimal Degrees and Recursively Inseparable Pairs of Recursively Enumerable Sets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (19-22):331-342.
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  14.  8
    K. Ambos-Spies & M. Lerman (1989). Lattice Embeddings Into the Recursively Enumerable Degrees. II. Journal of Symbolic Logic 54 (3):735-760.
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  15. Manuel Lerman (1972). On Suborderings of the Α-Recursively Enumerable Α-Degrees. Annals of Mathematical Logic 4 (4):369-392.
  16.  13
    Steffen Lempp & Manuel Lerman (1992). The Existential Theory of the Poset of R.E. Degrees with a Predicate for Single Jump Reducibility. 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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  17.  9
    C. G. Jockusch Jr, M. Lerman, R. I. Soare & R. M. Solovay (1989). Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion. Journal of Symbolic Logic 54 (4):1288 - 1323.
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  18. Manuel Lerman & Gerald E. Sacks (1972). Some Minimal Pairs of Α-Recursively Enumerable Degrees. Annals of Mathematical Logic 4 (4):415-442.
  19.  17
    Steffen Lempp & Manuel Lerman (1995). A General Framework for Priority Arguments. Bulletin of Symbolic Logic 1 (2):189-201.
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  20.  7
    Steffen Lempp & Manuel Lerman (1997). Iterated Trees of Strategies and Priority Arguments. Archive for Mathematical Logic 36 (4-5):297-312.
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  21.  4
    M. Lerman & J. B. Remmel (1984). The Universal Splitting Property. II. Journal of Symbolic Logic 49 (1):137-150.
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  22.  11
    Manuel Lerman (1970). Turing Degrees and Many-One Degrees of Maximal Sets. Journal of Symbolic Logic 35 (1):29-40.
  23.  5
    Manuel Lerman (1973). Admissible Ordinals and Priority Arguments. In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York,Springer-Verlag 311--344.
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  24.  11
    Manuel Lerman (1974). Least Upper Bounds for Minimal Pairs of |Alpha-R.E. |Alpha Degrees. Journal of Symbolic Logic 39 (1):49 - 56.
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  25. Manuel Lerman (1986). Degrees Which Do Not Bound Minimal Degrees. Annals of Pure and Applied Logic 30 (3):249-276.
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  26.  13
    Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp & Manuel Lerman (1996). Decidability of the Two-Quantifier Theory of the Recursively Enumerable Weak Truth-Table Degrees and Other Distributive Upper Semi-Lattices. 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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  27.  8
    Manuel Lerman (1969). Some Nondistributive Lattices as Initial Segments of the Degrees of Unsolvability. Journal of Symbolic Logic 34 (1):85-98.
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  28.  1
    C. T. Chong & M. Lerman (1976). Hyperhypersimple α-r.e. sets. Annals of Mathematical Logic 9 (1-2):1-48.
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  29.  11
    Manuel Lerman & James H. Schmerl (1979). Theories with Recursive Models. Journal of Symbolic Logic 44 (1):59-76.
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  30.  5
    Manuel Lerman (1976). Types of Simple Α-Recursively Enumerable Sets. Journal of Symbolic Logic 41 (2):419-426.
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  31.  6
    William C. Calhoun & Manuel Lerman (2001). Embedding Finite Lattices Into the Ideals of Computably Enumerable Turing Degrees. 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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  32.  2
    Manuel Lerman (1976). Congruence Relations, Filters, Ideals, and Definability in Lattices of Α-Recursively Enumerable Sets. Journal of Symbolic Logic 41 (2):405-418.
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  33. Manuel Lerman (1976). Ideals of Generalized Finite Sets in Lattices of Α‐Recursively Enumerable Sets. Mathematical Logic Quarterly 22 (1):347-352.
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  34.  2
    Sc Kleene, El Post, M. Kline, M. Lerman, L. Lowenheim, D. Normann, P. Odifreddi, G. Peano, Cs Peirce & R. Penrose (1999). R. PETER [1934] Uber den Zussammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann. In Edward R. Griffor (ed.), Handbook of Computability Theory. Elsevier 34.
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  35.  1
    Manuel Lerman & Richard Watnick (2003). Computable Choice Functions for Computable Linear Orderings. 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.  1
    Mannel Lerman (1978). On Elementary Theories of Some Lattices or Α-Recursively Enumerable Sets. Annals of Mathematical Logic 14 (3):227-272.
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  37.  1
    M. Lerman (1985). [Omnibus Review]. Journal of Symbolic Logic 50 (2):550-552.
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  38.  1
    Burkhard Englert, Manuel Lerman & Kevin Wald (2003). Homomorphisms and Quotients of Degree Structures. 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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  39. Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, James H. Schmerl & Reed Solomon (2008). Self-Embeddings of Computable Trees. 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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  40. L. Harrington, R. I. Soare, J. F. Knight & M. Lerman (1998). Griffor, ER, See Rathjen, M. Annals of Pure and Applied Logic 94:297.
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  41. C. G. Jockusch, M. Lerman, R. I. Soare & R. M. Solovay (1989). Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion. Journal of Symbolic Logic 54 (4):1288-1323.
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  42.  8
    M. Lerman (2010). A Framework for Priority Arguments. Cambridge University Press.
    This book presents a unifying framework for using priority arguments to prove theorems in computability.
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  43. M. Lerman (1985). Jockusch Carl G. Jr., and Posner David B.. Double Jumps of Minimal Degrees. Journal of Symbolic Logic 50 (2):550-552.
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  44. Manuel Lerman (1974). Least Upper Bounds for Minimal Pairs of Α-R.E. Α-Degrees. Journal of Symbolic Logic 39 (1):49-56.
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  45. M. Lerman, J. H. Schmerl & R. I. Soare (eds.) (1981). Logic Year 1979-80, the University of Connecticut, Usa. Springer-Verlag.
     
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  46. Manuel Lerman (1991). Minimal Degrees and Recursively Inseparable Pairs of Recursively Enumerable Sets. Mathematical Logic Quarterly 37 (19‐22):331-342.