5 found
  1.  14
    Members of countable π10 classes.Douglas Cenzer, Peter Clote, Rick L. Smith, Robert I. Soare & Stanley S. Wainer - 1986 - Annals of Pure and Applied Logic 31:145-163.
  2.  17
    On the ranked points of a Π1 0 set.Douglas Cenzer & Rick L. Smith - 1989 - Journal of Symbolic Logic 54 (3):975-991.
    This paper continues joint work of the authors with P. Clote, R. Soare and S. Wainer (Annals of Pure and Applied Logic, vol. 31 (1986), pp. 145--163). An element x of the Cantor space 2 ω is said have rank α in the closed set P if x is in $D^\alpha(P)\backslash D^{\alpha + 1}(P)$ , where D α is the iterated Cantor-Bendixson derivative. The rank of x is defined to be the least α such that x has rank α in (...)
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  3.  10
    Effective aspects of profinite groups.Rick L. Smith - 1981 - Journal of Symbolic Logic 46 (4):851-863.
    Profinite groups are Galois groups. The effective study of infinite Galois groups was initiated by Metakides and Nerode [8] and further developed by LaRoche [5]. In this paper we study profinite groups without considering Galois extensions of fields. The Artin method of representing a finite group as a Galois group has been generalized by Waterhouse [14] to profinite groups. Thus, there is no loss of relevance in our approach.The fundamental notions of a co-r.e. profinite group, recursively profinite group, and the (...)
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  4.  9
    Addendum to “Countable algebra and set existence axioms”.Harvey M. Friedman, Stephen G. Simpson & Rick L. Smith - 1984 - Annals of Pure and Applied Logic 28 (3):319-320.
  5.  8
    Decidable regularly closed fields of algebraic numbers.Louden Dries & Rick L. Smith - 1985 - Journal of Symbolic Logic 50 (2):468 - 475.