Many of the papers listed below can be found online. Due to the copyright agreements with the editors, these texts may differ from the published version. Please, always consult also the printed version. (OA) labels journals that are Open Access.
Generic sets and arbitrary objects Nous. To appear.
A topological semantics for reflexive insensitive modal logics (with Can Baskent and Dave Gilbert) Journal of Logic and Computation. To appear.
Ecumenical Propositional Tableaux (with Marcelo Coniglio Renato Reis Leme and Bruno Lopes) Studia Logica. 113, pp. 539-566, 2025.
A formal model for afthairetic modality (with Pedro Yago), Journal of Philosophical Logic, 53, pp. 1027-1065, 2024.
ZF and its intepretations. (with Santiago Jockwich and Sourav Tarafder), Annals of Pure and Applied Logic, 175(6), pp. 1-38, 2024.
How to make (mathematical) assertions with directives. (with Luca San Mauro and Laura Caponetto). Synthese, 202(127), pp. 1-16, 2024.
What model companionship can say about the Continuum Problem. (with Matteo Viale). Review of Symbolic Logic, 17(2), pp. 546-585, 2024.
Axioms and postulates as speech acts. (with Joao Vitor Schmidt). Erkenntnis, 89, pp. 3183-3202, 2024.
Formal ontology and mathematics. A case study on the identity of proofs (with Matteo Bianchetti). Topoi, 42, pp. 307-321, 2023.
Second order arithmetic as the model companion of set theory (with Matteo Viale). Archive for Mathematical Logic. 62, pp. 29-53, 2023.
Thin objects are not transparent. (with Matteo Plebani and Luca San Mauro). Theoria, 89(3), pp. 314–325, 2023.
Independence proofs in non-classical set theory (with Sourav Tarafder), Review of Symbolic Logic, 16(4), pp. 979-1010, 2023.
Fine's Postulationism, objectivity, and mathematical creation (with João Vitor Schmidt). Noesis, 39, pp. 123-138, 2022.
Many-valued logics and Suszkian modalities (with Edson Bezerra). Logic and Logical Philosophy, 31(4), pp. 611--636, 2022.
Ideal objects for set theory (with Santiago Jockwich and Sourav Tarafder), Journal of Philosophical Logic, 51, pp. 583--602, 2022.
ZF between classicality and non-classicality (with Sourav Tarafder), Studia Logica, 110, pp. 189-218, 2022.
Logic of ignorance and being wrong (with Dave Gilbert, Mattia Petrolo, and Ekaterina Kubitchkina), Logic Journal of the IGPL. 30(5), pp. 870--885, 2022.
What is it to believe in a mathematical assertion (with Luca San Mauro), Rivista Italiana di Filosofia del Linguaggio, 15(1), pp. 154-157, 2021. (OA)
Squeezing argument and the plurality of informal notions (with Edson Bezerra), Journal of Applied Logic, 8(7), pp. 1899-1916, 2021. (OA)
Reflexive-insensitive logics, the box-dot translation, and the modal logic of generic absoluteness (with David Gilbert), Notre Dame Journal of Formal Logic, 62(2), pp. 269-283, 2021.
Non-classical models of ZF (with Santiago Jockwich Martinez), Studia Logica, 109, pp. 509-537, 2021.
On negation for non classical set theories (with Santiago Jockwich Martinez), Journal of Philosophical Logic, 50, pp. 549-570, 2021.
A non-standard Kripke semantics for the minimal deontic logic (with Edson Bezerra), Logic and Logical Philosophy, 30, pp.125-135, 2021. (OA)
Speech acts in mathematics (with Marco Ruffino and Luca San Mauro), Synthese. Online first, 22 July 2020.
Tableaux for essence and contingency (with Pedro Yago), Logic Journal of the IGPL. Online first, 13 May 2020.
A note on logics of essence and accident (with David Gilbert), Logic Journal of the IGPL. 28(5), pp. 881-891, 2020.
On forms of justification in set theory (with Neil Barton and Claudio Ternullo). Australasian Journal of Logic. 17(4), pp. 158-200, 2020. (OA)
At Least One Black Sheep: Pragmatics and Mathematical Language. (with Marco Ruffino and Luca San Mauro, with a response by Aarne Ranta), Journal of Pragmatics, 160, pp. 114-119, 2020.
Rejoinder. (with Marco Ruffino and Luca San Mauro, in response to Aarne Ranta's comments on At Least One Black Sheep: Pragmatics and Mathematical Language), Journal of Pragmatics, 160, pp. 123, 2020.
Infinite forcing and the generic multiverse, Studia Logica, 108, pp. 277–290, 2020.
Genericity and arbitrariness, Logique & Analyse, 62(248), pp. 435-452, 2019.
New axioms in set theory (with Matteo Viale), Matematica, Cultura e Società - Rivista dell'Unione Matematica Italiana, 3(3), pp, 211--236, 2018.
A direct proof of the five element basis theorem (with Boban Veličković), Mathematical Logic Quarterly, 63(3-4), pp. 289–298, 2017.
A note on the introduction of Hilbert’s Grundlagen der Geometrie, Manuscrito, 40(2): 5–17, 2017. (OA)
A neighborhood semantics for the logics of unknown truths and of false beliefs (with David Gilbert), Australasian Journal of Logic, 14(1), pp. 246–267, 2017. (OA)
Reflexive insensitive modal logics, (with David Gilbert) Review of Symbolic Logic, 9(1), pp. 167–180, 2016.
Preservation of Suslin trees and side conditions, Journal of Symbolic Logic, 81(2), pp. 483–492, 2016.
Hilbert between the formal and the informal sides of mathematics, Manuscrito, 38(2), pp.5–45, 2015. (OA)
The foundation of set theory between theory and practice, Philosophia Scientiae, 18(1), pp. 45–80, 2014.
Hilbert, completeness and geometry, RIFAJ, 2(2), pp. 80–102, 2011. (Reprinted in: RIFAJ, 9(2), pp. 152–180, 2018.) (OA)
A logic of isolation (with with Can Baskent and Dave Gilbert) Logic, Language, Information, and Computation 30th International Workshop, WoLLIC 2024. To appear.
Coq Formalization of a Tableau for the Classical-Intuitionistic Propositional Fragment of Ecumenical Logic (with Renato Leme and Bruno Lopez) Proceedings of the 3rd Brazilian Workshop of Logic, pp. 25--32, 2022.
From Plato to Weil and beyond: Genericity through the history of mathematics (with Renato Leme), Khronos, 10, pp. 140--158, 2020.
Cantor e l'infinito, Lettera Matematica Pristem, 107, pp. 61--69, 2018. [In Italian]
On weak existence in set theory. (with Neil Barton) In Palgrave Companion for the Philosophy of Set Theory (Antos-Kuby, Barton, Venturi eds.), Palgrave 2025.
Linear models and set theory. (with Santiago Jockwich Martinez), in Seminário Permanente Lógica no Avião, (E. Almeida, A. Costa-Leite, and R. Freire eds.), Série n, pp. 9–21, 2019. (OA)
On the naturalness of new axioms in set theory, in Logic and its Philosophy: contemporary trends in Latin America and Spain, (Fernández de Castro, Freund, Ruffino eds.), College Publications, pp. 117–142, 2018.
Forcing, multiverse and realism, in Objectivity, Knowledge and Proof. FilMat Studies in the Philosophy of Mathematics, (Boccuni, Sereni eds.) pp. 211–241, Boston Study in the Philosophy of Science, Springer. 2016.
Naturalness in mathematics (with Luca San Mauro), in From Logic to Practice. Italian studies in the philosophy of mathematics, (Lolli, Panza, Venturi eds.) Boston Studies in the Philosophy of Science, Springer, pp. 277–313, 2015.
Proper forcing remastered (with Boban Veličković), in Appalachian Set Theory (Cummings, Schimmerling eds.), London Mathematical Society lecture notes series, Cambridge University Press, pp. 331–362, 2013.
Editor (with Luca Incurvati) Oxford Handbook in the Philosophy of Set Theory, Oxford University Press. To appear.
Editor (with Carolin Antos-Kuby and Neil Barton) Palgrave companion of Philosophy of Set Theory Palgrave, 2025.
Editor (with Mattia Petrolo) Paradoxes Between Truth and Proof Synthese Library, Springer, 2025.
Editor (with Gabriele Lolli and Marco Panza) of the volume From Logic to Practice. Italian studies in the philosophy of mathematics Boston Studies in the Philosophy of Science, Springer, 2015.
Guest editor (with Joan Bagaria, Juliette Kennedy, Claudio Ternullo) of the issue What can philosophy do for set theory Journal of Philosophical Logic. To appear.
Guest editor (with Giorgio Sbardolini) of the issue Filosofia della Matematica 2(2), RIFAJ, 2011.
2010 The Proper Forcing Axiom: a tutotial. Notes from the tutorial of J. T. Moore held at the Young Set Theory Workshop 2010. On J.T. Moore’s webpage: http://www.math.cornell.edu/ justin/
2009 Forcing Axiom and the Continuum Hypothesis. Master thesis. On M. Viale’s webpage: http://www.logicatorino.altervista.org/matteo viale/
2019, (with Felipe Albarelli) for Manuscrito, review of Linnebo, Philosophy of Mathematics, Princeton University Press, 2017.
2017, for Mathematical Reviews, review of W. Ewald and W. Sieg eds. David Hilbert’s lectures on the foundations of arithmetic and logic (1917–1933), Springer, 2013.
2018, review for Mathematical Reviews of Golshani and Hayut’s On Foreman’s Maximality Principle, Journal of Symbolic Logic, 81(4):1344–1356, 2016.
2018, review for Mathematical Reviews of R. Kahle Sets, truth and recursion, in “Unifying the Philosophy of Truth”, (D. Achourioti, K. Fujimoto, H. Galinon, and J. Martinez eds. eds.) Springer, 2015.
2017, review for Mathematical Reviews of Z. Weber On Paraconsistent Downward LöwenheimSkolem Theorems, in “The logica yearbook 2015”, (P. Arazim and M. Dancak eds.) College Publications, 2016.
2017, review for Mathematical Reviews of J. Leo, Coordinate-free logic, Review of Symbolic Logic 9(3):522–555, 2016.
2017, review for Mathematical Reviews of A. Blum, An aspect of necessity, Metalogicon (N.S.)( 1), pp. 31–36, 2016.
2017, review for Mathematical Reviews of R. Ciuni, Conjunction in paraconsistent weak Kleene logic, in “The logica yearbook 2014”, (P. Arazim and M. Dancak eds.) College Publications, 2015.
2016, review for Mathematical Reviews of J. Burgess Intuition of three kinds in Gödel’s view on the continuum, in “Interpreting Gödel. Critical Essays” (J. Kennedy ed.) Cambridge University Press, 2016.
2016, review for Mathematical Reviews of V. Dimonte and L. Wu, A general tool for consistency results related to I1, European Journal of Mathematics 2(2), 474-492, 2016.