15 found
Order:
  1.  6
    Type Theories, Toposes and Constructive Set Theory: Predicative Aspects of AST.Ieke Moerdijk & Erik Palmgren - 2002 - Annals of Pure and Applied Logic 114 (1-3):155-201.
    We introduce a predicative version of topos based on the notion of small maps in algebraic set theory, developed by Joyal and one of the authors. Examples of stratified pseudotoposes can be constructed in Martin-Löf type theory, which is a predicative theory. A stratified pseudotopos admits construction of the internal category of sheaves, which is again a stratified pseudotopos. We also show how to build models of Aczel-Myhill constructive set theory using this categorical structure.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   18 citations  
  2.  7
    Wellfounded Trees in Categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.
    In this paper we present and study a categorical formulation of the W-types of Martin-Löf. These are essentially free term algebras where the operations may have finite or infinite arity. It is shown that W-types are preserved under the construction of sheaves and Artin gluing. In the proofs we avoid using impredicative or nonconstructive principles.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   15 citations  
  3.  3
    Aspects of Predicative Algebraic Set Theory I: Exact Completion.Benno van den Berg & Ieke Moerdijk - 2008 - Annals of Pure and Applied Logic 156 (1):123-159.
    This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on realizability [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory II: Realizability, Theoret. Comput. Sci. . Available from: arXiv:0801.2305, 2008], and the other on sheaves [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory III: Sheaf models, 2008 ]. We introduce the notion of a predicative category with small (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   7 citations  
  4.  2
    A Model for Intuitionistic Non-Standard Arithmetic.Ieke Moerdijk - 1995 - Annals of Pure and Applied Logic 73 (1):37-51.
    This paper provides an explicit description of a model for intuitionistic non-standard arithmetic, which can be formalized in a constructive metatheory without the axiom of choice.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   9 citations  
  5.  15
    Minimal Models of Heyting Arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
  6. On Choice Sequences Determined by Spreads.Gerritder Hoeven & Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (3):908 - 916.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  7.  4
    Derived Rules for Predicative Set Theory: An Application of Sheaves.Benno van den Berg & Ieke Moerdijk - 2012 - Annals of Pure and Applied Logic 163 (10):1367-1383.
  8.  26
    Heine-Borel Does Not Imply the Fan Theorem.Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (2):514-519.
  9.  11
    Sheaf Models for Choice Sequences.Gerrit Van Der Hoeven & Ieke Moerdijk - 1984 - Annals of Pure and Applied Logic 27 (1):63-107.
  10.  12
    On Choice Sequences Determined by Spreads.Gerrit van der Hoeven & Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (3):908 - 916.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  11.  34
    Compositionality and the Analysis of Anaphora.Fred Landman & Ieke Moerdijk - 1983 - Linguistics and Philosophy 6 (1):89 - 114.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  12.  3
    On the Freyd Cover of a Topos.Ieke Moerdijk - 1983 - Notre Dame Journal of Formal Logic 24 (4):517-526.
  13.  5
    The Axiom of Multiple Choice and Models for Constructive Set Theory.Benno van den Berg & Ieke Moerdijk - 2014 - Journal of Mathematical Logic 14 (1):1450005.
  14. Nijmegen, The Netherlands July 27–August 2, 2006.Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis - 2007 - Bulletin of Symbolic Logic 13 (2).
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  15. Minimal Models of Heyting Arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
    Direct download  
     
    Export citation  
     
    My bibliography