Publications
2020
Scholarly publications
van Oosten, J., & de Jong, T. (2020). The Sierpinski Object in the Scott Realizability Topos. Logical Methods in Computer Science, 16(3), 1-16. https://doi.org/10.23638/LMCS-16(3:12)2020
https://dspace.library.uu.nl/bitstream/handle/1874/413128/1904.13354.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/413128/1904.13354.pdf?sequence=1
2018
Scholarly publications
Moerdijk, I., & van Oosten, J. (2018). Sets, models and proofs: Provides a concise introduction to mathematical logic for mathematics students. Springer. https://doi.org/10.1007/978-3-319-92414-4
van Oosten, J., & Voorneveld, N. (2018). Extensions of Scott's Graph Model and Kleene's Second Algebra. Indagationes Mathematicae, 29(1), 5-22. https://doi.org/10.1016/j.indag.2017.05.008
2016
Scholarly publications
van Oosten, J., & Zou, T. (2016). Classical and relative realizability. Theory and Applications of Categories, 31(22), 571-593. http://www.tac.mta.ca/tac/volumes/31/22/31-22abs.html
https://dspace.library.uu.nl/bitstream/handle/1874/347485/classical.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/347485/classical.pdf?sequence=1
Faber, E., & van Oosten, J. (2016). Effective Operations of type 2 in PCAs. Computability, 5(2), 127-146. https://doi.org/10.3233/COM-150048
2014
Scholarly publications
van Oosten, J. (2014). Review of "Homotopy Type Theory". The bulletin of symbolic logic, 20(4), 497-500.
van Oosten, J., & Faber, E. (2014). More on Geometric Morphisms between Realizability Toposes. Theory and Applications of Categories, 29(30), 874-895.
https://dspace.library.uu.nl/bitstream/handle/1874/307583/29_30.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/307583/29_30.pdf?sequence=1
van Oosten, J. (2014). Realizability with a Local Operator of A.M. Pitts. Theoretical Computer Science, 546(27), 237-243. https://doi.org/10.1016/j.tcs.2014.03.011
van Oosten, J. (2014). A Notion of Homotopy for the Effective Topos. Mathematical Structures in Computer Science, 1-15. https://doi.org/10.1017/S096012951400053X
2013
Scholarly publications
Lee, S., & van Oosten, J. (2013). Basic Subtoposes of the Effective Topos. Annals of Pure and Applied Logic, 164, 866-883. https://doi.org/10.1016/j.apal.2013.04.001
van Oosten, J. (2013). Boekbespreking van "Proofs and Computations". Nieuw archief voor wiskunde. Serie 5, 14, 290-290.
2011
Scholarly publications
van Oosten, J. (2011). Partial Combinatory Algebras of Functions. Notre Dame Journal of Formal Logic, 52(4), 431-448. https://doi.org/10.1215/00294527-1499381
https://dspace.library.uu.nl/bitstream/handle/1874/234501/PartialcombinatoryVanOosten.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/234501/PartialcombinatoryVanOosten.pdf?sequence=1
Professional publications
van Oosten, J. (2011). Stephen G. Simpson. Subsystems of Second Order Arithmetic (second edition) . Cambridge: Cambridge University Press, 2009. Perspectives In Logic. 444 p., prijs £53.00 ISBN 9780521884396. Nieuw archief voor wiskunde. Serie 5, 12(3), 219-219.
https://dspace.library.uu.nl/bitstream/handle/1874/234503/simpsonreview.pdf?sequence=2
https://dspace.library.uu.nl/bitstream/handle/1874/234503/simpsonreview.pdf?sequence=2
2008
Scholarly publications
van Oosten, J. (2008). Realizability: an Introduction to its Categoriacal Side. (Studies in Logic ed.) Elsevier.
2006
Scholarly publications
van Oosten, J. (2006). A general form of relative recursion. Notre Dame Journal of Formal Logic, 47(3), 311-318.
Hoffmann, M., van Oosten, J., & Streicher, T. (2006). Well-foundedness in realizability. Archive for Mathematical Logic, 45, 795-805.
van Oosten, J. (2006). Filtered Colimits in the effective topos. Journal of Pure and Applied Algebra, 205, 446-451.
Professional publications
van Oosten, J. (2006). Bookreview From Sets and Types to Topology and Analysis. Bulletin of Symbolic Logic, 12, 611-612.
van Oosten, J. (2006). J. Ponstein. Nonstandard Analysis. - Groningen : SOM Research School School, 2002. 147 p., ISBN 90-367-1672-1. Nieuw archief voor wiskunde. Serie 5, 7(3), 218. http://www.rug.nl/research/gradschool-economics-and-business/organization/publications/ponstein.pdf
2005
Scholarly publications
van Oosten, J., & Kouwenhoven-Gentil, C. A. K. (2005). Algebraic Set Theory and the Effective Topos. Journal of Symbolic Logic, 70(3), 879-890.
2004
Professional publications
van Oosten, J. (2004). Sheaves, Games and Model Completions. The bulletin of symbolic logic, 10, 216-217.
van Oosten, J. (2004). A Partial Analysis of Modified Realizability. Journal of Symbolic Logic, 69(2), 421-429.
2003
Scholarly publications
Hofstra, P. J. W., & van Oosten, J. (2003). Ordered partial combinatory algebras. In Mathematical Proceedings of the Cambridge Philosophical Society (pp. 445-463)
2002
Scholarly publications
Birkedal, L., & van Oosten, J. (2002). Relative and modified relative realizability. Annals of Pure and Applied Logic, 118(1-2), 115-132.
van Oosten, J. (2002). Realizability: a historical essay. Mathematical Structures in Computer Science, 12, 239-263.
Other output
van Oosten, J. (2002). A partial analysis of Modified Realizability. Paper presented at Unknown event.
2000
Scholarly publications
van Oosten, J. (2000). Fibrations and Calculi of Fractions. Journal of Pure and Applied Algebra, 146, 77-102.
van Oosten, J., & Simpson, A. K. (2000). Axioms and (Counter)examples in Synthetic Domain Theory. Annals of Pure and Applied Logic, 104(1-3), 233-278.
1999
Scholarly publications
van Oosten, J. (1999). History and Developments. In L. Birkedal, J. van Oosten, G. Rosolini, & D. S. Scott (Eds.), Preliminary Proceedings for the Tutorial Workshop on Realizability and Applications Elsevier.
van Oosten, J. (1999). Introduction to Peano Arithmetic. Communications of the Mathematical Institute, Rijksuniversiteit Utrecht, 21, i-58.
van Oosten, J. (1999). A Combinatory Algebra for Sequential functionals of Finite Type. In S. B. Cooper, & J. K. Truss (Eds.), Models and Computability (pp. 389-406). (LMS Lecture Series in Mathematics; No. 259). Cambridge University Press.
1997
Scholarly publications
van Oosten, J. (1997). Extensional realizability. Annals of Pure and Applied Logic, 84(3), 317-349.
van Oosten, J. (1997). A combinatory algebra for sequential functionals of finite type. In S. Barry Cooper, & J. K. Truss (Eds.), Models and computability (pp. 389-405). Campridge University Press.
van Oosten, J. (1997). The modified realizability topos. Journal of Pure and Applied Algebra, 116(1-3), 273-289.
1996
Scholarly publications
van Oosten, J. (1996). Two remarks on the Lifschitz Realizability Topos. Journal of Symbolic Logic, 61(1), 70-79.
van Oosten, J. (1996). Topological Aspects of Traces. In J. Billington, & W. Reisig (Eds.), Applications and Theory of Petri Nets 1996 (pp. 480-496). Springer.
1994
Scholarly publications
van Oosten, J. (1994). Axiomatizing Higher-Order Kleene Realizability. Annals of Pure and Applied Logic, 70, 87-111.
1991
Scholarly publications
van Oosten, J. (1991). A semantical Proof of De Jongh's Theorem. Archive for Mathematical Logic, 31, 105-114.
van Oosten, J. (1991). Extension of Lifschitz' Realizability to Higher-Order Arithmetic, and a Solution to a problem of F. Richman. Journal of Symbolic Logic, 56(2), 964-973.
1990
Scholarly publications
van Oosten, J. (1990). Lischitz' Realizability. Journal of Symbolic Logic, 55(2), 805-821.