Publications
Publications
Book
From Sets and Types to Topology and Analysis: towards practicable foundations for constructive mathematics, with P. Schuster (eds.), Oxford University Press, Oxford Logic Guides 48, 2005, pp. xix+376. http://dx.doi.org/10.1093/acprof:oso/9780198566519.001.0001
Articles
Constructive type theory, an appetizer, forthcoming in "Higher Order Metaphysics", Fritz, P.; Jones, N. (eds.), Oxford University Press.
The entanglement of logic and set theory, constructively, in Critial Views of Logic, Mirja Hartimo, Frode Kjosavik, Øystein Linnebo (eds.), Routledge (2023).
Weyl and two kinds of potential domain, with Øystein Linnebo, Noûs (published online on 10 April 2023). https://doi.org/10.1111/nous.12457
Bishop's mathematics: a philosophical perspective, in "Handbook of Constructive Mathematics", Bridges, D.; Ishihara, H.; Rathjen, M.; Schwichtenberg, H. (eds.), Cambridge University Press, 2023.
Predicativity and constructive mathematics, in G. Oliveri, C. Ternullo and S. Boscolo (eds), “Objects, Structures, and Logics”, FilMat Studies in the Philosophy of Mathematics, Boston Studies in the Philosophy and History of Science, vol. 339, Springer, Cham, 2022, pp. 287—309. https://doi.org/10.1007/978-3-030-84706-7
The entanglement of logic and set theory, constructively, Inquiry, 2022, 65:6, pp. 638—659 https://doi.org/10.1080/0020174X.2019.1651080
Exploring Predicativity, in: “Proof, Computation, Digitalization in Mathematics”, Computer Science and Philosophy, editors Klaus Mainzer, Peter Schuster and Helmut Schwichtenberg, World Scientific, 2018, https://doi.org/10.1142/9789813270947_0003
Predicativity and Feferman, in: G. Jaeger and W. Sieg (eds.), Feferman and Foundations, Springer’s book series “Outstanding Contributions to Logic”, 2018, https://link.springer.com/chapter/10.1007/978-3-319-63334-3_15
Matematica Costruttiva, AphEx, “Portale Italiano di Filosofia Analitica”, June 2016, available at http://www.aphex.it/index.php?Temi=557D03012202740321040507777327.
Error and Predicativity, In: A. Beckmann, V. Mitrana, M. Soskova, eds., Evolving Computability, Lecture Notes in Computer Science, Volume 9136, 2015, pp 13–22. https://doi.org/10.1007/978-3-319-20028-6_2
Finite methods in mathematical practice, with Peter Schuster, In: G. Link, ed., Formalism and Beyond: On the Nature of Mathematical Discourse. Logos, De Gruyter, Boston, 2014, pp. 351–398. https://doi.org/10.1515/9781614518471.351
A generalised cut characterisation of the fullness axiom in CZF, with Erik Palmgern and Peter Schuster, Log. J. IGPL 21, 2013, pp. 63–76. https://doi.org/10.1093/jigpal/jzs022
Transitive Closure is conservative over weak operational set theory, with Andrea Cantini, in U. Berger, H. Diener, P. Schuster, M. Seisenberger (eds.), Logic, Construction, Computation, Ontos Verlag, Frankfurt, Germany, 2012. https://doi.org/10.1515/9783110324921.91
A tutorial for Minlog, version 5.0, with Monika Seisenberger and Helmut Schwichtenberg, 2011, pp. 44. (Distributed with the proof assistant Minlog 5.0).
On French and Krause’s “Identity in Physics”, with Elena Castellani, in D. Howard, B. van Fraassen, O. Bueno, Elena Castellani, S. French and D. Krause, The Physics and Metaphysics of Identity and Individuality, Metascience, 2011. https://doi.org/10.1007/s11016-010-9463-7
Elementary Constructive Operational Set Theory, with Andrea Cantini, in Ways of Proof Theory, ed. R. Schindler, Ontos Series in Mathematical Logic, Ontos Verlag, Frankfurt, Germany, 2010. https://doi.org/10.1515/9783110324907.199
Constructive and intuitionistic ZF, in: Stanford Encyclopedia of Philosophy, E. Zalta (ed.), Center for the Study of Language and Information, Stanford University, 2009, available at http://plato.stanford.edu/entries/set-theory-constructive/ (substantive revisions in 2014).
Constructive set theory with operations, with A. Cantini, in: A. Andretta, K. Kearnes, D. Zambella eds., Logic Colloquium 2004, Association of Symbolic Logic, Lecture notes in Logic, 29, 2008, pp. 47-83.
Binary refinement implies discrete exponentiation, with Peter Aczel, Hajime Ishihara, Erik Palmgren, Peter Schuster, Studia Logica, 84, 2006, pp. 367–374. https://link.springer.com/article/10.1007/s11225-006-9014-9
Constructive notions of sets (Part I) Sets in Martin–Löf type theory, in Annali del Dipartimento di Filosofia, Università degli Studi di Firenze, Nuova serie XI, Firenze University Press 2006, pp. 347–387.
On constructing completions, with Hajime Ishihara and Peter Schuster, in Journal of Symbolic Logic, 70, 2005, pp. 969–978. https://doi.org/10.2178/jsl/1122038923
Inaccessible set axioms may have little consistency strength, with M. Rathjen, Annals of Pure and Applied Logic, Vol 115/1-3, pp. 33-70, 2002. https://doi.org/10.1016/S0168-0072(01)00083-5