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

I am also running a two-years research project (2018-2020) funded by the Austrian Science Fund (FWF), entitled *Classifying relations via computable reducibility*.

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

**Classifying Equivalence relations in the Ershov hierarchy**

(with N. Bazhenov, M. Mustafa, A. Sorbi, M. Yamaleev), submitted**Bi-embeddability spectra and bases of spectra**

(with E. Fokina and D. Rossegger), submitted**Computable bi-embeddable categoricity**

(with N. Bazhenov, E. Fokina, and D. Rossegger)

forthcoming in*Algebra and Logic***Measuring the complexity of reductions between equivalence relations**

(with E. Fokina and D. Rossegger)

forthcoming in*Computability***Trial and error mathematics: Completions of theories**

(with J. Amidei, U. Andrews, D. Pianigiani, and A. Sorbi)

forthcoming in*Journal of Logic and Computation***Degrees of bi-embeddable categoricity of equivalence structures**

(with N. Bazhenov, E. Fokina, and D. Rossegger)

forthcoming in*Archive for Mathematical Logic***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)

*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)

*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)

*Journal of Symbolic Logic*, 79, 60-88, 2014

**At least one black sheep: Pragmatics and the language of mathematics**

(with M. Ruffino and G. Venturi), submitted**Church-Turing thesis, in practice**

in M. Piazza and G. Pulcini (eds),*Truth, Existence and Explanation*, Boston Studies in the Philosophy of Science, Springer, 225-248, 2018**Direzioni della logica in Italia: la teoria (classica) della ricorsività**

(with P. Cintioli and A. Sorbi)

in H. Hosni, G. Lolli, C. Toffalori (eds.),*Le direzioni della ricerca logica in Italia 2*, Edizioni ETS, 195-234, 2018**Naturalness in mathematics**

(with G. Venturi)

in G. Lolli, M. Panza, and G. Venturi (eds.),*From Logic to Practice*, Boston Studies in the Philosophy and History of Science 308, Springer, 277-313, 2014

**Limit learning equivalence structures**

(with E. Fokina and T. Koetzing), submitted**Degree spectra of structures with respect to the bi-embeddability relation**

(with E. Fokina and D. Rossegger)

*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)

*Proceedings of the 11th Panhellenic Logic Symposium*, 126-132, 2017**Reducibility and bi-reducibility spectra of equivalence relations**

(with E. Fokina and D. Rossegger)

*Proceedings of the 11th Panhellenic Logic Symposium*, 83-89, 2017

**Speech acts in mathematics**

(with M. Ruffino and G. Venturi)**Instant equivalence relations and their (instant) complexity**

(with N. Bazhenov and A. Sorbi)

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