On this page I aim to collect links to recent, published and unpublished papers connected to realizability. Have you written anything new, and do you wish it to be included, send me the URL where it can be downloaded.
Sheaf Toposes for Realizability (pdf), Archive for Mathematical Logic 47,5 (2008),465--478.
The Realizability Approach to Computable Analysis and Topology, thesis.
On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos.
W-Types in the Effective Topos, note.
Aspects of Predicative Algebraic Set Theory II: Realizability, to appear in TCS.
Relative and Modified Relative Realizability, Annals of Pure and Applied Logic 118 (2002), 115-132
Concepts and Aims of Functional Interpretations (ps format), in: Löwe and Rudolph (eds), Foundations of the Formal Sciences, Kluwer 1999, pp.205--218
The intuitionistic arithmetical hierarchy, Logic Colloquium '99, pp. 51--59, Lect. Notes Log. 17.
Fragments of Heyting Arithmetic (ps format), J. Symbolic Logic 65 (2000), no. 3, 1223--1240.
Introduction to Turing Categories, APAL 156,2-3 (2008),183--209.
Bounded Modified Realizability, Journal of Symbolic Logic 71 (2006), 329--346
Well-foundedness in Realizability
Archive for Mathematical Logic 45 (2006), 795--805Relative Completions, JPAA 192, 1-3 (2004), 129--148
Completions in Realizability (Thesis)
All realizability is relative, Math.Proc.Camb.Phil.Soc. 141 (2006), 239--264
Ordered PCA's, Math.Proc.Camb.Phil.Soc.134 (2003),445-463.
Variations on Realizability--ps.gz file,Math.Struct.Comp.Sci. 12 (2002)
Algebraic Set Theory and the Effective Topos--ps.gz file, Journ.Symb.Log.70(3) (2005),879-890
Comparing Realizability over Pw and K2--ps.gz file
Impredicativity entails Untypedness--ps.gz file
From constructive mathematics to computable analysis via the realizability interpretation (PhD thesis)--link to pdf
Realizability toposes and language semantics, thesis (1995), University of Edinburgh, available as ECS-LFCS-95,332
Unifying Typed and Untyped Realizability, note--text file
The sequentially realizable functionals, APAL 117,1-3 (2002),1--93
On the ubiquity of certain total type structures, MSCS 17,5 (2007),841--953
A uniform approach to domain theory in realizability models. MSCS 7 (1997), 469--505.
An abstract look at realizability--ps file, final version published by Robinson and Rosolini in CSL 2001, LNCS 2142.
Full Abstraction and Universality via Realisability--ps.gz file
A Characterization of the Left Exact Categories whose Exact Completions are Toposes--link.
Journal of pure and applied algebra 177, 287-301, 3, 2003.
Exact Completions and Toposes, thesis--pdf file
Läuchli's Completeness Theorem from a Topos-theoretic perspective, Applied Categorical Structures 2008.
A Strongly Normalising Curry-Howard Correspondence for IZF Set Theory pdf file
Also in: CSL 2003, pp.441-454.
Normalization of IZF with Replacement ps file
Also (shorter) in: CSL 2006,LNCS 4207 (Springer), pp.516--530
Hierarchies in Intuitionistic Arithmeticps file
Classical and Intuitionistic Hierarchies in Extended Intuitionistic Analysisps file
Realizability: a historical essay, Math.Struct.Comp.Sci. 12 (2002), 239-263
A Partial Analysis of Modified Realizability, Journ.Symb.Log. 69 (2004),2,421-429
Filtered Colimits in the Effective Topos Journ. Pure Appl.Alg. 205 (2006), 446--451
A general form of relative recursion,Notre Dame Journal od Formal Logic 47(3) (2006), 311-318
Partial Combinatory Algebras of Functions, may 2009.
Tripos Theory in Retrospect,Math.Struct.Comp.Sci. 12 (2002).
CZF has the Disjunction and Numerical Existence Property,Journal of Symbolic Logic 70 (2005) 1233-1254.
Constructive set theory and Brouwerian principles, Journal of Universal Computer Science, Vol. 11, No. 12 (2005) 2008-2033.
Choice principles in constructive and classical set theories, Lecture Notes in Logic 27 (2006) 299-326.
Realizability for Constructive Zermelo-Fraenkel Set Theory, Logic Colloquium 2003. Lecture Notes In Logic 141 (2006) 442-471.
Metamathematical Properties of Intuitionistic Set Theories with Choice Principles, in: Cooper, Loewe, Sorbi: New Computational Paradigms (Springer 2008) 84-98.
Solving Recursive Domain Equations in Models of Intuitionistic Set Theory--ps.gz file
A Note on ``Extensional PERs''--pdf file
A Semantic Version of the Diller-Nahm Variant of Gödel's Dialectica Interpretation--ps.gz file
Generalising Realizability and Heyting Models for Constructive Set Theory--pdf document; talk presented at 3d Workshop on Formal Topology, Padova, May 2007
Diplomarbeit (in German), München 2007
To Jaap van Oosten.