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  1.  12
    J. C. E. Dekker (1971). Countable Vector Spaces with Recursive Operations. Part II. Journal of Symbolic Logic 36 (3):477-493.
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  2.  14
    J. C. E. Dekker (1969). Countable Vector Spaces with Recursive Operations. Part I. Journal of Symbolic Logic 34 (3):363-387.
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  3.  6
    J. C. E. Dekker (1971). Two Notes on Vector Spaces with Recursive Operations. Notre Dame Journal of Formal Logic 12 (3):329-334.
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  4.  12
    J. C. E. Dekker & E. Ellentuck (1989). Isols and the Pigeonhole Principle. Journal of Symbolic Logic 54 (3):833-846.
    In this paper we generalize the pigeonhole principle by using isols as our fundamental counting tool.
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  5.  17
    J. C. E. Dekker (1986). The Inclusion-Exclusion Principle for Finitely Many Isolated Sets. Journal of Symbolic Logic 51 (2):435-447.
    A nonnegative interger is called a number, a collection of numbers a set and a collection of sets a class. We write ε for the set of all numbers, o for the empty set, N(α) for the cardinality of $\alpha, \subset$ for inclusion and $\subset_+$ for proper inclusion. Let α, β 1 ,...,β k be subsets of some set ρ. Then α' stands for ρ-α and β 1 ⋯ β k for β 1 ∩ ⋯ ∩ β k . For (...)
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  6.  7
    J. C. E. Dekker (1981). Twilight Graphs. Journal of Symbolic Logic 46 (3):539-571.
    This paper deals primarily with countable, simple, connected graphs and the following two conditions which are trivially satisfied if the graphs are finite: (a) there is an edge-recognition algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to decide whether they are adjacent, (b) there is a shortest path algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to find a minimal path joining them. A graph $G = \langle\eta, \eta\rangle$ with η as set (...)
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  7.  5
    J. C. E. Dekker (1990). An Isolic Generalization of Cauchy's Theorem for Finite Groups. Archive for Mathematical Logic 29 (4):231-236.
    In his note [5] Hausner states a simple combinatorial principle, namely: $$(H)\left\{ {\begin{array}{*{20}c} {if f is a function a non - empty finite set \sigma into itself, p a} \\ {prime, f^p = i_\sigma and \sigma _0 the set of fixed points of f, then } \\ {\left| \sigma \right| \equiv \left| {\sigma _0 } \right|(mod p).} \\\end{array}} \right.$$ .He then shows how this principle can be used to prove:Fermat's little theorem,Cauchy's theorem for finite groups,Lucas' theorem for binomial numbers.Letε=(0,1, ...),ℱ (...)
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  8.  5
    J. C. E. Dekker (1986). Isols and Burnside's Lemma. Annals of Pure and Applied Logic 32 (3):245-263.
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  9.  2
    J. C. E. Dekker & E. Ellentuck (1992). Myhill's Work in Recursion Theory. Annals of Pure and Applied Logic 56 (1-3):43-71.
    In this paper we discuss the following contributions to recursion theory made by John Myhill: two sets are recursively isomorphic iff they are one-one equivalent; two sets are recursively isomorphic iff they are recursively equivalent and their complements are also recursively equivalent; every two creative sets are recursively isomorphic; the recursive analogue of the Cantor–Bernstein theorem; the notion of a combinatorial function and its use in the theory of recursive equivalence types.
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  10.  7
    C. H. Applebaum & J. C. E. Dekker (1970). Partial Recursive Functions and Ω-Functions. Journal of Symbolic Logic 35 (4):559-568.
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  11.  3
    J. C. E. Dekker (1981). Automorphisms of $\Omega$-Cubes. Notre Dame Journal of Formal Logic 22 (2):120-128.
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  12.  3
    J. C. E. Dekker (1978). Projective Bigraphs with Recursive Operations. Notre Dame Journal of Formal Logic 19 (2):193-199.
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  13. J. C. E. Dekker (1960). Review: Anil Nerode, Extensions to Isols. [REVIEW] Journal of Symbolic Logic 25 (4):359-361.
     
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  14. J. C. E. Dekker (1957). Review: J. Myhill, J. C. Shepherdson, Effective Operations on Partial Recursive Functions. [REVIEW] Journal of Symbolic Logic 22 (3):303-303.
     
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  15.  1
    J. C. E. Dekker & E. Ellentuck (1974). Recursion Relative to Regressive Functions. Annals of Mathematical Logic 6 (3-4):231-257.
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  16.  2
    J. C. E. Dekker (1966). Review: John Myhill, Recursive Equivalence Types and Combinatorial Functions. [REVIEW] Journal of Symbolic Logic 31 (3):510-511.
  17.  4
    J. C. E. Dekker (1982). Automorphisms of $\Omega$-Octahedral Graphs. Notre Dame Journal of Formal Logic 23 (4):427-434.
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  18.  3
    J. C. E. Dekker (1976). Projective Planes of Infinite but Isolic Order. Journal of Symbolic Logic 41 (2):391-404.
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  19.  1
    J. C. E. Dekker (1962). Review: Hao Wang, Alternative Proof of a Theorem of Kleene. [REVIEW] Journal of Symbolic Logic 27 (1):81-82.
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  20.  1
    J. C. E. Dekker (1996). Myhill John. Recursive Equivalence Types and Combinatorial Functions. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Nagel Ernest, Suppes Patrick, and Tarski Alfred, Stanford University Press, Stanford, Calif., 1962, Pp. 46–55. [REVIEW] Journal of Symbolic Logic 31 (3):510-511.
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  21. J. C. E. Dekker (1967). Review: Arnold Oberschelp, Ein Satz uber die Unlosbarkeitsgrade der Mengen von Naturlichen Zahlen. [REVIEW] Journal of Symbolic Logic 32 (1):124-124.
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  22. J. C. E. Dekker (1964). Review: J. P. Cleave, Creative Functions. [REVIEW] Journal of Symbolic Logic 29 (2):102-103.
     
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  23. Kenneth Appel & J. C. E. Dekker (1966). Infinite Series of Isols. Journal of Symbolic Logic 31 (4):652.
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  24. J. C. E. Dekker (1964). Cleave J. P.. Creative functions. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 7 , pp. 205–212. [REVIEW] Journal of Symbolic Logic 29 (2):102-103.
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  25. J. C. E. Dekker (1969). Countable Vector Spaces with Recursive Operations Part I1. Journal of Symbolic Logic 34 (3):363-387.
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  26. J. C. E. Dekker (1957). Myhill J. And Shepherdson J. C.. Effective Operations on Partial Recursive Functions. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathetnatik, Vol. 1 , Pp. 310–317. [REVIEW] Journal of Symbolic Logic 22 (3):303.
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  27. J. C. E. Dekker (1960). Nerode Anil. Extensions to Isols. Annals of Mathematics, Second Series, Vol. 73 , Pp. 362–403. Journal of Symbolic Logic 25 (4):359-361.
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  28. J. C. E. Dekker (1967). Oberschelp Arnold. Ein Satz über die Unlösbarkeitsgrade der Mengen von natürlichen Zahlen. Abhandlungen der Braunschweigische Wissenschaftliche Gesellschaft , vol. 12 , pp. 1–3. [REVIEW] Journal of Symbolic Logic 32 (1):124.
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  29. J. C. E. Dekker (1962). Wang Hao. Alternative Proof of a Theorem of Kleene. Journal of Symbolic Logic 27 (1):81-82.
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