33 found
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  1. A new proof that analytic sets are Ramsey.Erik Ellentuck - 1974 - Journal of Symbolic Logic 39 (1):163-165.
    We give a direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey.
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  2. Incompatible extensions of combinatorial functions.Erik Ellentuck - 1983 - Journal of Symbolic Logic 48 (3):752-755.
    We find necessary and sufficient conditions for compatibility of the Myhill and the Nerode extensions of a combinatorial function to the isols.
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  3.  19
    Hyper-Torre isols.Erik Ellentuck - 1981 - Journal of Symbolic Logic 46 (1):1-5.
    If T is an isol let D(T) be the least set of isols which contains T and is closed under predecessors and the application of almost recursive combinatorial functions. We find an infinite regressive isol T such that the universal theory (with respect to recursive relations and almost recursive combinatorial functions) of D(T) is the same as that of the nonnegative integers.
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  4. A coding theorem for isols.Erik Ellentuck - 1970 - Journal of Symbolic Logic 35 (3):378-382.
  5.  26
    Categoricity regained.Erik Ellentuck - 1976 - Journal of Symbolic Logic 41 (3):639-643.
  6. Review: J. C. E. Dekker, The Minimum of Two Regressive Isols. [REVIEW]Erik Ellentuck - 1967 - Journal of Symbolic Logic 32 (4):527-527.
  7. Incompleteness via simple sets.Erik Ellentuck - 1971 - Notre Dame Journal of Formal Logic 12 (2):255-256.
  8.  25
    Decomposable Isols and Their Degrees.Erik Ellentuck - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):251-260.
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  9.  13
    J. C. E. Dekker. The minimum of two regressive isols. Mathematische Zeitschrift, vol. 83 , pp. 345–366.Erik Ellentuck - 1968 - Journal of Symbolic Logic 32 (4):527.
  10.  23
    Galois Theorems for Isolated Fields.Erik Ellentuck - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (1):1-9.
  11.  22
    Extensions of Isolic Models.Erik Ellentuck - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):323-333.
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  12.  5
    Degrees of isolic theories.Erik Ellentuck - 1973 - Notre Dame Journal of Formal Logic 14 (3):331-340.
  13.  16
    The positive properties of isolic integers.Erik Ellentuck - 1972 - Journal of Symbolic Logic 37 (1):114-132.
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  14.  14
    Decomposable Isols and Their Degrees.Erik Ellentuck - 1976 - Mathematical Logic Quarterly 22 (1):251-260.
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  15.  12
    Galois Theorems for Isolated Fields.Erik Ellentuck - 1981 - Mathematical Logic Quarterly 27 (1):1-9.
  16.  13
    An algebraic difference between isols and cosimple isols.Erik Ellentuck - 1972 - Journal of Symbolic Logic 37 (3):557-561.
    There is a fairly simple algebraic property that distinguishes isols from cosimple isols.
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  17.  11
    Random isols.Erik Ellentuck - 1983 - Mathematical Logic Quarterly 29 (1):1-6.
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  18.  33
    The Representation of Cardinals in Models of Set Theory.Erik Ellentuck - 1968 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):143-158.
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  19.  10
    Extensions of Isolic Models.Erik Ellentuck - 1971 - Mathematical Logic Quarterly 17 (1):323-333.
  20.  10
    A $Delta^0_2$ Theory of Regressive Isols.Erik Ellentuck - 1974 - Journal of Symbolic Logic 39 (3):459-468.
    We examine the action of unary $\Delta^0_2$ functions on the regressive isols. A manageable theory is produced and we find that such a function maps $\Lambda_R$ into $\Lambda$ if and only if it is eventually $R\uparrow$ increasing and maps $\Lambda_R$ into $\Lambda_R$ if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to $\Lambda_R$.
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  21.  9
    A Δ02 theory of regressive isols.Erik Ellentuck - 1974 - Journal of Symbolic Logic 39 (3):459 - 468.
    We examine the action of unary Δ 0 2 functions on the regressive isols. A manageable theory is produced and we find that such a function maps Λ R into Λ if and only if it is eventually $R\uparrow$ increasing and maps Λ R into Λ R if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to Λ R.
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  22.  6
    Barback J.. Recursive functions and regressive isols. Mathematica Scandinavica, vol. 15 , pp. 29–42.Erik Ellentuck - 1967 - Journal of Symbolic Logic 32 (2):269-270.
  23.  6
    Review: John Myhill, Recursive Function Theory. [REVIEW]Erik Ellentuck - 1968 - Journal of Symbolic Logic 33 (4):619-620.
  24.  5
    Myhill John. Ω — Λ. Recursive function theory, Proceedings of symposia in pure mathematics, vol. 5, American Mathematical Society, Providence 1962, pp. 97–104. [REVIEW]Erik Ellentuck - 1969 - Journal of Symbolic Logic 33 (4):619-620.
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  25.  6
    A Non‐Representation Theorem for Gödel‐Bernays Set Theory.Erik Ellentuck - 1970 - Mathematical Logic Quarterly 16 (6):341-345.
  26.  18
    The foundations of suslin logic.Erik Ellentuck - 1975 - Journal of Symbolic Logic 40 (4):567-575.
  27.  25
    A choice free theory of dedekind cardinals.Erik Ellentuck - 1969 - Journal of Symbolic Logic 34 (1):70-84.
  28.  7
    Almost combinatorial Skolem functions.Erik Ellentuck - 1970 - Journal of Symbolic Logic 35 (1):65-72.
  29.  4
    Model theoretic methods in the theory of isols.Erik Ellentuck - 1978 - Annals of Mathematical Logic 14 (3):273-285.
  30.  2
    Nonrecursive combinatorial functions.Erik Ellentuck - 1972 - Journal of Symbolic Logic 37 (1):90-95.
  31.  2
    Review: J. Barback, Recursive Functions and Regressive Isols. [REVIEW]Erik Ellentuck - 1967 - Journal of Symbolic Logic 32 (2):269-270.
  32.  6
    The Representation of Cardinals in Models of Set Theory.Erik Ellentuck - 1968 - Mathematical Logic Quarterly 14 (7‐12):143-158.
  33.  33
    Diagonal Methods in the Theory of Isols.Erik Ellentuck - 1980 - Mathematical Logic Quarterly 26 (13):193-204.