On this page I aim to collect links to recent, published and unpublished papers connected to realizability.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.
Learning, Realizability and Games in Classical Arithmetic (pdf), Ph.D. thesis, March-April 2011
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.
Arithmetic is Categorical, May 2011. Submitted to TAC.
Dialectica Interpretations - A Categorical Analysis, thesis.
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.
Effective Operations of Type 2 in PCAs. Computability 5 (2016), pp.127-146.
More on Geometric Morphisms between Realizability Toposes.
Theory and Applications of Categories vol. 29, no. 30 (2014), pp. 874-895.
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)
The Sierpinski Object in the Scott Realizability Topos--pdf file. Submitted to Logical Methods in Computer Science.
Algebraic Set Theory and the Effective Topos--ps.gz file, Journ.Symb.Log.70(3) (2005),879-890
Basic Subtoposes of the Effective Topos--pdf file. Annals of Pure and Applied Logic 164 (2013), 866-883
Comparing Realizability over Pw and K2--pdf 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. pdf file.
On the ubiquity of certain total type structures, MSCS 17,5 (2007),841--953. pdf file.
Computability structures, simulations and realizability, May 2011, pdf file.
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
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes--pdf 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, Notre Dame Journal of Formal Logic 52(4) (2011), 431-448
A notion of Homotopy for the Effective Topos, March 2010.
Realizability with a Local Operator of A.M. Pitts, Theoretical Computer Science 546 (2014), 237-243.
Classical and Relative Realizability, Theory and Applications of Categories 31 (2016), 22, pp.571--593.
Extensions of Scott's Graph Model and Kleene's Second Algebra, October 2016. Indagationes Mathematicae 29 (2018), pp.5--22.
The Theory of Triposes, Ph.D. thesis, Cambridge 1981.
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.
Preuves, Types et Sous-Types, thesis, ps file.
Solving Recursive Domain Equations in Models of Intuitionistic Set Theory--ps.gz file
A Note on ``Extensional PERs''--pdf file, J. Pure Appl. Algebra 215 (2011), no. 3, 253–256.
Regular Functors and Relative Realizability Categories--pdf file, accepted for MSCS
Realizability Catgories--pdf file, thesis.(submitted).
A Semantic Version of the Diller-Nahm Variant of Gödel's Dialectica Interpretation--ps.gz file
Krivine's Classical Realizability from a Categorical Perspective pdf file
A Classical Realizability Model arising from a Stable Model of Untyped Lambda Calculus pdf 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.