### My current research project investigates ways to confirm/conceptually justify strong axioms of infinity (large cardinal axioms) incompatible with the Axiom of Choice, and also examines their consequences on other foundational issues. The consistency of these axioms implies that a different scenario, based on Woodin's Ultimate-L conjecture, must be false and, as a consequence, that we may still be very far from attaining a definitive reduction of (set-theoretic) incompleteness. Assuming both the consistency and the conceptual justifiability of choiceless large cardinals, a concrete possibility is that there really are absolutely undecidable statements in set theory, as a consequence of the fact that the continuation of the large-cardinal hierarchy into the choiceless large-cardinal hierarchy suggests, as hinted at by Gödel, that mathematics (set theory) is inexhaustible.

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### Over the years, I have researched the following topics: the Continuum Hypothesis (history and philosophy of), the justification of new axioms, the set-theoretic multiverse, mathematical Platonism, abstraction principles, logical fallacies, and topics in the history of logic.

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Ongoing Project:

- 'Self-Similarity, Large Cardinals and Incompleteness', funded by a Marie-Curie Seal of Excellence Romanian funding scheme (PNRR-I3-C9-2022. Contract n. 35195). Start Date: 01/01/2024 - End Date: 31/12/2025. Department of Philosophy, University Babeș-Bolyai of Cluj-Napoca. Role: Project Director.

Past Projects:

Barcel

- ‘Mathematical and Philosophical Aspects of a Multiversist Foundation of Set Theory’, funded by the Beatriu de Pinós Fellowship [Marie-Skłodowska Curie Actions] n. 00192 BP2018. (01/02/2020-30/06/2023), Department of Mathematics and Computer Science, University of Barcelona (supervisor: Prof Joan Bagaria). Role: Principal Investigator.

Participation In Other Projects (as Post-Doc):

- 'Set Theory at a Crossroads: Proving the HOD Conjecture' Europa Excelencia n. EUR 2022-134032 . PI: Prof Joan Bagaria. Location: University of Barcelona (01/07/2023-31/12/2023). Role: Post-Doctoral Fellow.

- ‘Lógica Matemática’, Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia Number: MTM-PID2020-116773GB-I00. PI: Prof. Enrique Casanovas and Prof. Joan Bagaria, University of Barcelona (01/09/2021-31/08/2024). Role: Associate Researcher.

- ‘The Hyperuniverse Programme‘, funded by the FWF Stand-Alone Grant (Fonds zur Förderung der wissenschaftlichen Forschung) n. P28420. PI: Prof. Sy-David Friedman, Kurt Gödel Research Center for Mathematical Logic, University of Vienna (01/04/2016-31/03/2021). Role: Collaborator.

- ‘University of Tartu’s 'ASTRA project PER ASPERA', funded by the European Regional Development Fund, ID: 2014-2020.4.-01.16-0027. PI: Prof. Bruno Mölder, Department of Philosophy, University of Tartu (01/01/2018-31/08/2022). Role: Post-Doctoral Fellow.

- ‘The Hyperuniverse. The Laboratory of the Infinite’, funded by the John Templeton Foundation Grant ID #35216. PI: Prof. Sy-David Friedman (01/01/2013-30/09/2015), Kurt Gödel Research Center for Mathematical Logic, University of Vienna. Role: Post-Doctoral Fellow.