Results for 'Gerald E. Sacks'

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  1.  6
    Higher recursion theory.Gerald E. Sacks - 1990 - New York, NY, USA: Cambridge University Press.
    This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
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  2.  30
    Saturated model theory.Gerald E. Sacks - 1972 - Reading, Mass.,: W. A. Benjamin.
    This book contains the material for a first course in pure model theory with applications to differentially closed fields.
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  3.  25
    Bounds on Weak Scattering.Gerald E. Sacks - 2007 - Notre Dame Journal of Formal Logic 48 (1):5-31.
    The notion of a weakly scattered theory T is defined. T need not be scattered. For each a model of T, let sr() be the Scott rank of . Assume sr() ≤ ω\sp A \sb 1 for all a model of T. Let σ\sp T \sb 2 be the least Σ₂ admissible ordinal relative to T. If T admits effective k-splitting as defined in this paper, then θσ\cal Aθ\cal A$ a model of T.
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  4.  34
    Metarecursive sets.G. Kreisel & Gerald E. Sacks - 1965 - Journal of Symbolic Logic 30 (3):318-338.
    Our ultimate purpose is to give an axiomatic treatment of recursion theory sufficient to develop the priority method. The direct or abstract approach is to keep in mind as clearly as possible the methods actually used in recursion theory, and then to formulate them explicitly. The indirect or experimental approach is to look first for other mathematical theories which seem similar to recursion theory, to formulate the analogies precisely, and then to search for an axiomatic treatment which covers not only (...)
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  5.  11
    The limits of E-recursive enumerability.Gerald E. Sacks - 1986 - Annals of Pure and Applied Logic 31:87-120.
  6.  12
    Effective forcing versus proper forcing.Gerald E. Sacks - 1996 - Annals of Pure and Applied Logic 81 (1-3):171-185.
    , a notion of forcing over E, the E-closure of L, is said to be effective if every sideways -generic extension preserves E-closure. There are set notions of forcing in E that do not preserve E-closure. The main theorem below asserts that is effective if and only if it is locally proper, a weak variant of Shelah's notion of proper.
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  7.  2
    Selected logic papers.Gerald E. Sacks - 1999 - River Edge, N.J.: World Scientific.
    Contents: Recursive Enumerability and the Jump Operator; On the Degrees Less Than 0'; A Simple Set Which Is Not Effectively Simple; The Recursively Enumerable Degrees Are Dense; Metarecursive Sets (with G Kreisel); Post's Problem, Admissible Ordinals and Regularity; On a Theorem of Lachlan and Marlin; A Minimal Hyperdegree (with R O Gandy); Measure-Theoretic Uniformity in Recursion Theory and Set Theory; Forcing with Perfect Closed Sets; Recursion in Objects of Finite Type; The a-Finite Injury Method (with S G Simpson); Remarks Against (...)
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  8. Kreisel, Generalized.Gerald E. Sacks - 1996 - In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel. A K Peters. pp. 103.
  9.  11
    Liu Shih-Chao. A note on many-one reducibility.Gerald E. Sacks - 1966 - Journal of Symbolic Logic 31 (3):512.
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  10.  9
    Liu Shih-Chao. On many-one degrees.Gerald E. Sacks - 1996 - Journal of Symbolic Logic 31 (3):512-513.
  11. Measure-theoretic uniformity.Gerald E. Sacks - 1969 - In Kurt Gödel, Jack J. Bulloff, Thomas C. Holyoke & Samuel Wilfred Hahn (eds.), Foundations of Mathematics. New York: Springer. pp. 51--57.
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  12.  1
    Preface.Gerald E. Sacks - 1972 - Annals of Mathematical Logic 4 (4):341.
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  13.  7
    Shih-Chao Liu. On many-one degrees. The journal of symbolic logic, vol. 28 no. 2 , pp. 143–153.Gerald E. Sacks - 1966 - Journal of Symbolic Logic 31 (3):512-513.
  14.  7
    Atomic models higher up.Jessica Millar & Gerald E. Sacks - 2008 - Annals of Pure and Applied Logic 155 (3):225-241.
    There exists a countable structure of Scott rank where and where the -theory of is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its -theory. Most well-known models with unbounded atoms below also realize a non-principal -type; such a model that preserves the Σ1-admissibility of will have Scott rank . Makkai [M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 301–318. [4]] produces a hyperarithmetical model of Scott (...)
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  15.  4
    Metarecursive Sets.G. Kreisel & Gerald E. Sacks - 1968 - Journal of Symbolic Logic 33 (4):622-623.
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  16.  22
    Review: J. R. Shoenfield, J. W. Addison, Leon Henkin, Alfred Tarski, Applications of Model Theory to Degrees of Unsolvability. [REVIEW]Gerald E. Sacks - 1972 - Journal of Symbolic Logic 37 (3):610-611.
  17.  6
    A. H. Lachlan. The impossibility of finding relative complements for recursively enumerable degrees. The journal of symbolic logic, vol. 31 , pp. 434–454. [REVIEW]Gerald E. Sacks - 1971 - Journal of Symbolic Logic 36 (3):539-540.
  18.  9
    Friedberg R. M.. The fine structure of degrees of unsolvability of recursively enumerable sets. Summaries of talks presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, 2nd edn., Communications Research Division, Institute for Defense Analyses, Princeton, N.J., 1960, pp. 404–406. [REVIEW]Gerald E. Sacks - 1963 - Journal of Symbolic Logic 28 (2):166-166.
  19.  20
    Ihrig Ann H.. The Post-Lineal theorems for arbitrary recursively enumerable degrees of unsolvability. Notre Dame journal of formal logic, vol. 6 no. 1 , pp. 54–72. [REVIEW]Gerald E. Sacks - 1968 - Journal of Symbolic Logic 32 (4):529-529.
  20.  14
    J. R. Shoenheld. Applications of model theory to degrees of unsolvability. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, edited by J. W. Addison, Leon Henkin, and Alfred Tarski, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 359–363. [REVIEW]Gerald E. Sacks - 1972 - Journal of Symbolic Logic 37 (3):610-611.
  21. Review: Ann H. Ihrig, The Post-Lineal Theorems for Arbitrary Recursively Enumerable Degrees of Unsolvability. [REVIEW]Gerald E. Sacks - 1967 - Journal of Symbolic Logic 32 (4):529-529.
  22.  5
    Review: A. H. Lachlan, The Impossibility of Finding Relative Complements for Recursively Enumerable Degrees. [REVIEW]Gerald E. Sacks - 1971 - Journal of Symbolic Logic 36 (3):539-540.
  23.  19
    Richard M. Friedberg and Hartley RogersJr., Reducibility and completeness for sets of integers. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 5 , pp. 117–125. [REVIEW]Gerald E. Sacks - 1960 - Journal of Symbolic Logic 25 (4):362-363.
  24.  13
    Review: R. M. Friedberg, The Fine Structure of Degrees of Unsolvability of Recursively Enumerable Sets. [REVIEW]Gerald E. Sacks - 1963 - Journal of Symbolic Logic 28 (2):166-166.
  25.  7
    Review: Shih-Chao Liu, A Note on Many-One Reducibility. [REVIEW]Gerald E. Sacks - 1966 - Journal of Symbolic Logic 31 (3):512-512.
  26.  5
    Review: Shih-Chao Liu, On Many-One Degrees. [REVIEW]Gerald E. Sacks - 1966 - Journal of Symbolic Logic 31 (3):512-513.
  27.  7
    Shoenfield J. R.. On degrees of unsolvability. Annals of mathematics, second series, vol. 69 , pp. 644–653.Shoenfield J. R.. An uncountable set of incomparable degrees. Proceedings of the American Mathematical Society, vol. 11 , pp. 61–62. [REVIEW]Gerald E. Sacks - 1964 - Journal of Symbolic Logic 29 (4):203-204.
  28.  15
    Generalized recursion theory II: proceedings of the 1977 Oslo symposium.Jens Erik Fenstad, R. O. Gandy & Gerald E. Sacks (eds.) - 1978 - New York: sole distributors for the U.S.A. and Canada, Elsevier North-Holland.
    GENERALIZED RECUBION THEORY II © North-Holland Publishing Company (1978) MONOTONE QUANTIFIERS AND ADMISSIBLE SETS Ion Barwise University of Wisconsin ...
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  29.  18
    Gerald E. Sacks. On a theorem of Lachlan and Martin. Proceedings of the American Mathematical Society, vol. 18 , pp. 140–141. [REVIEW]C. E. M. Yates - 1968 - Journal of Symbolic Logic 32 (4):529.
  30.  17
    Gerald E. Sacks. A maximal set which is not complete. Michigan mathematical journal, vol. 11 , pp. 193–205.K. Appel - 1968 - Journal of Symbolic Logic 32 (4):528.
  31.  4
    The quantum particle illusion: conceptual quantum mechanics.Gerald E. Marsh - 2022 - New Jersey: World Scientific.
    Problems with the conceptual foundations of quantum mechanics date back to attempts by Max Born, Niels Bohr, Werner Heisenberg, as well as many others in the 1920s to continue to employ the classical concept of a particle in the context of the quantum world. The experimental observations at the time and the assumption that the classical concept of a particle was to be preserved have led to an enormous literature on the foundations of quantum mechanics and a great deal of (...)
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  32.  12
    Review: Gerald E. Sacks, A Maximal Set which is not Complete. [REVIEW]K. Appel - 1967 - Journal of Symbolic Logic 32 (4):528-528.
  33.  17
    Review: Gerald E. Sacks, Forcing with Perfect Closed Sets. [REVIEW]J. R. Shoenfield - 1974 - Journal of Symbolic Logic 39 (2):330-330.
  34.  25
    Gerald E. Sacks. Recursive enumerability and the jump operator. Transactions of the American Mathematical Society, vol. 108 , pp. 223–239. [REVIEW]Donald L. Kreider - 1964 - Journal of Symbolic Logic 29 (4):204.
  35.  14
    Gerald E. Sacks. Degrees of unsolvability. Annals of Mathematics studies, no. 55. Lithoprinted. Princeton University Press, Princeton1963, xii + 174 pp. [REVIEW]Gustav B. Hensel - 1964 - Journal of Symbolic Logic 29 (4):202-203.
  36.  8
    Gerald E. Sacks. On suborderings of degrees of recursive unsolvability. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 7 , pp. 46–56. [REVIEW]Gustav B. Hensel - 1964 - Journal of Symbolic Logic 29 (4):203.
  37. Review: Gerald E. Sacks, On Suborderings of Degrees of Recursive Unsolvability. [REVIEW]Gustav B. Hensel - 1964 - Journal of Symbolic Logic 29 (4):203-203.
  38. Review: Gerald E. Sacks, Degrees of Unsolvability. [REVIEW]Gustav B. Hensel - 1964 - Journal of Symbolic Logic 29 (4):202-203.
  39.  22
    Facts and Values.Gerald E. Myers - 1965 - Philosophy and Phenomenological Research 26 (2):280-281.
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  40.  24
    Gerald E. Sacks. On the degrees less than 0′. Annals of mathematics, second series, vol. 77 , pp. 211–231. - Gerald E. Sacks. Correction to “On the degrees less than 0′.”Annals of mathematics, second series, vol. 78 , p. 204. [REVIEW]Marian Boykan Pour-El - 1964 - Journal of Symbolic Logic 29 (1):60.
  41. Review: Gerald E. Sacks, On the Degrees Less than 0'. [REVIEW]Marian Boykan Pour-El - 1964 - Journal of Symbolic Logic 29 (1):60-60.
  42.  8
    Gerald E. Sacks. Higher recursion theory. Perspectives in mathematical logic. Springer-Verlag, Berlin etc. 1990, xv + 344 pp. [REVIEW]Dag Normann - 1992 - Journal of Symbolic Logic 57 (2):761-762.
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  43.  7
    Review: Gerald E. Sacks, Higher Recursion Theory. [REVIEW]Dag Normann - 1992 - Journal of Symbolic Logic 57 (2):761-762.
  44.  32
    Gerald E. Sacks. Metarecursively enumerable sets and admissible ordinals. Bulletin of the American Mathematical Society, vol. 72 , pp. 59–64. - Gerald E. Sacks. Post's problem, admissible ordinals, and regularity. Transactions of the American Mathematical Society, vol. 124 , pp. 1–23. - Gerald E. Sacks. Metarecursion theory. Sets, models and recursion theory, Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, edited by John N. Crossley, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, pp. 243–263. - Graham C. DriscollJr., Metarecursively enumerable sets and their metadegrees. The Journal of symbolic logic, vol. 33 , pp. 389–11. [REVIEW]Richard A. Platek - 1969 - Journal of Symbolic Logic 34 (1):115-116.
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  45.  9
    Gerald E. Sacks. Saturated model theory. Photolithographed from typewritten manuscript. Advanced book program. W. A. Benjamin, Inc., Reading, Mass., 1972, xiv + 335 pp. [REVIEW]Michael Makkai - 1975 - Journal of Symbolic Logic 40 (4):637-640.
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  46.  11
    Review: Gerald E. Sacks, Saturated Model Theory. [REVIEW]Michael Makkai - 1975 - Journal of Symbolic Logic 40 (4):637-640.
  47.  20
    Gerald E. Sacks. Recursion in objects of finite type. Actes du Congrès International des Mathématiciens 1970, Gauthier-Villars, Paris 1971, Vol. 1, pp. 251–254. [REVIEW]D. A. Clarke - 1974 - Journal of Symbolic Logic 39 (2):343-344.
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  48.  12
    Review: Gerald E. Sacks, Recursion in Objects of Finite Type. [REVIEW]D. A. Clarke - 1974 - Journal of Symbolic Logic 39 (2):343-344.
  49.  8
    In memoriam: Gerald E. Sacks, 1933–2019.Manuel Lerman & Theodore A. Slaman - 2022 - Bulletin of Symbolic Logic 28 (1):150-155.
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  50.  23
    G. Kreisel and Gerald E. Sacks. Metarecursive sets. The journal of symbolic logic, vol. 30 , pp. 318–338.Richard A. Platek - 1968 - Journal of Symbolic Logic 33 (4):622-623.
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