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  1. Benno van den Berg & Ieke Moerdijk (2014). The Axiom of Multiple Choice and Models for Constructive Set Theory. Journal of Mathematical Logic 14 (1):1450005.
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  2. Benno van den Berg & Ieke Moerdijk (2012). Derived Rules for Predicative Set Theory: An Application of Sheaves. Annals of Pure and Applied Logic 163 (10):1367-1383.
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  3. Benno Van Den Berg & Ieke Moerdijk (2008). Aspects of Predicative Algebraic Set Theory I: Exact Completion. 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 (...)
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  4. Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis (2007). Nijmegen, The Netherlands July 27–August 2, 2006. Bulletin of Symbolic Logic 13 (2).
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  5. Ieke Moerdijk & Erik Palmgren (2002). Type Theories, Toposes and Constructive Set Theory: Predicative Aspects of AST. 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.
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  6. Ieke Moerdijk & Erik Palmgren (2000). Wellfounded Trees in Categories. 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.
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  7. Ieke Moerdijk & Erik Palmgren (1997). Minimal Models of Heyting Arithmetic. Journal of Symbolic Logic 62 (4):1448-1460.
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  8. Ieke Moerdijk (1995). A Model for Intuitionistic Non-Standard Arithmetic. 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.
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  9. Gerrit van der Hoeven & Ieke Moerdijk (1984). On Choice Sequences Determined by Spreads. Journal of Symbolic Logic 49 (3):908 - 916.
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  10. Gerritder Hoeven & Ieke Moerdijk (1984). On Choice Sequences Determined by Spreads. Journal of Symbolic Logic 49 (3):908 - 916.
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  11. Ieke Moerdijk (1984). Heine-Borel Does Not Imply the Fan Theorem. Journal of Symbolic Logic 49 (2):514-519.
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  12. Gerrit van der Hoeven & Ieke Moerdijk (1984). On Choice Sequences Determined by Spreads. Journal of Symbolic Logic 49 (3):908-916.
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  13. Gerrit Van Der Hoeven & Ieke Moerdijk (1984). Sheaf Models for Choice Sequences. Annals of Pure and Applied Logic 27 (1):63-107.
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  14. Fred Landman & Ieke Moerdijk (1983). Compositionality and the Analysis of Anaphora. Linguistics and Philosophy 6 (1):89 - 114.
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  15. Ieke Moerdijk (1983). On the Freyd Cover of a Topos. Notre Dame Journal of Formal Logic 24 (4):517-526.
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