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Manuel Lerman [25]M. Lerman [15]Mannel Lerman [1]
  1. 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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  2. 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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  3. Carl G. Jockusch Jr, 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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  4. 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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  5. 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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  6. Burkhard Englert, Manuel Lerman & Kevin Wald (2003). Homomorphisms and Quotients of Degree Structures. Annals of Pure and Applied Logic 123 (1-3):193-233.
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  7. Manuel Lerman & Richard Watnick (2003). Computable Choice Functions for Computable Linear Orderings. Mathematical Logic Quarterly 49 (5):485-510.
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  8. 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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  9. 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.
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  10. 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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  11. 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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  12. 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.
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  13. 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.
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  14. 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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  15. 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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  16. Steffen Lempp & Manuel Lerman (1995). A General Framework for Priority Arguments. Bulletin of Symbolic Logic 1 (2):189-201.
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  17. 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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  18. Manuel Lerman (1991). Minimal Degrees and Recursively Inseparable Pairs of Recursively Enumerable Sets. Mathematical Logic Quarterly 37 (19‐22):331-342.
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  19. 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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  20. 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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  21. 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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  22. Manuel Lerman (1986). Degrees Which Do Not Bound Minimal Degrees. Annals of Pure and Applied Logic 30 (3):249-276.
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  23. M. Lerman (1985). [Omnibus Review]. Journal of Symbolic Logic 50 (2):550-552.
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  24. M. Lerman (1985). Upper Bounds for the Arithmetical Degrees. Annals of Pure and Applied Logic 29 (3):225-254.
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  25. M. Lerman & J. B. Remmel (1984). The Universal Splitting Property. II. Journal of Symbolic Logic 49 (1):137-150.
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  26. M. Lerman (1983). Degrees of Unsolvability: Local and Global Theory. Springer-Verlag.
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  27. 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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  28. Manuel Lerman & James H. Schmerl (1979). Theories with Recursive Models. Journal of Symbolic Logic 44 (1):59-76.
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  29. 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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  30. C. T. Chong & M. Lerman (1976). Hyperhypersimple α-r.e. sets. Annals of Mathematical Logic 9 (1-2):1-48.
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  31. 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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  32. 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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  33. Manuel Lerman (1976). Types of Simple Α-Recursively Enumerable Sets. Journal of Symbolic Logic 41 (2):419-426.
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  34. 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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  35. Manuel Lerman (1973). Admissible Ordinals and Priority Arguments. In. In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York,Springer-Verlag. 311--344.
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  36. Manuel Lerman (1972). On Suborderings of the Α-Recursively Enumerable Α-Degrees. Annals of Mathematical Logic 4 (4):369-392.
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  37. Manuel Lerman & Gerald E. Sacks (1972). Some Minimal Pairs of Α-Recursively Enumerable Degrees. Annals of Mathematical Logic 4 (4):415-442.
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  38. 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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  39. Manuel Lerman (1970). Turing Degrees and Many-One Degrees of Maximal Sets. Journal of Symbolic Logic 35 (1):29-40.
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  40. 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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