I am a postdoctoral fellow at the Institute for Discrete Mathematics and Geometry at Vienna University of Technology.

My research interests lie in computability theory and philosophy of mathematics.

- "Trial and error mathematics: Completions of theories" (with J. Amidei, U. Andrews, D. Pianigiani, and A. Sorbi), submitted
- "At least one black sheep: Pragmatics and the language of mathematics" (with M. Ruffino and G. Venturi), submitted
- "Degrees of bi-embeddable categoricity of equivalence structures" (with N. Bazhenov, E. Fokina, and D. Rossegger), submitted
- "Trial and error mathematics II:
Dialectical sets and quasidialectical sets, their degrees,
and their distribution within the class of limit sets"
(with J. Amidei, D. Pianigiani and A. Sorbi),
*The Review of Symbolic Logic*, 9(4), 810--835, 2016 - "Trial and error mathematics I:
Dialectical and quasidialectical systems"
(with J. Amidei, D. Pianigiani, G. Simi,
and A. Sorbi),
*The Review of Symbolic Logic*, 9(2), 299--324, 2016 - Universal computably enumerable equivalence relations"
(with U. Andrews, S. Lempp, J.S. Miller,
K.M. Ng, and A. Sorbi),
*The Journal of Symbolic Logic*, 79, 60--88, 2014

- "Church-Turing thesis, in practice", forthcoming
in M. Piazza and G. Pulcini (eds),
*Truth, Existence and Explanation*, Boston Studies in the Philosophy of Science, Springer - "Direzioni della logica in Italia: la teoria
(classica) della ricorsività" (with P. Cintioli and A. Sorbi),
forthcoming in H. Hosni, G. Lolli, C. Toffalori (eds.),
*Direzioni della logica in Italia*, Edizioni della Normale - "Naturalness in mathematics" (with G. Venturi),
in G. Lolli et al. (eds.),
*From Logic to Practice*, Boston Studies in the Philosophy and History of Science 308, Springer, 277--313, 2014

- "Degree Spectra of Structures with Respect to the
Bi-embeddability Relation" (with E. Fokina and
D. Rossegger), in
*Proceedings of the 11th Panhellenic Logic Symposium*, 32--38, 2017 - "Computable bi-embeddable categoricity of equivalence
structures" (with N. Bazhenov, E. Fokina,
and D. Rossegger), in
*Proceedings of the 11th Panhellenic Logic Symposium*, 126--132, 2017 - "Reducibility and bi-reducibility spectra of equivalence
relations" (with E. Fokina and D. Rossegger),
in
*Proceedings of the 11th Panhellenic Logic Symposium*, 83--89, 2017

- "Bi-embeddability spectra that do not collapse to isomorphism spectra" (with E. Fokina and D. Rossegger)
- "Measuring the complexity of reductions between equivalence relations" (with E. Fokina and D. Rossegger)
- "Bi-embeddable categoricity of structures" (with N. Bazhenov, E. Fokina, and D. Rossegger)
- "Speech acts in mathematics" (with M. Ruffino and G. Venturi)
- "On the complexity of arithmetical binary relations"

Institute of Discrete Mathematics and Geometry

Vienna University of Technology

Wiedner Hauptstrasse 8-10/104

1040 Vienna, Austria

email: luca.san.mauro(at)tuwien.ac.at

phone: (+43)665-65101427