Claudio Ternullo has earned two PhDs in Philosophy (Pisa, 2005 and Liverpool, 2012). Currently, he is Beatriu de Pinós (Marie-Skłodowska Curie COFUND) Post-Doctoral Fellow at the University of Barcelona. Previously, he has held positions as post-doc at the Kurt Gödel Research Center for Mathematical Logic, University of Vienna and at the University of Tartu. His research interests lie in logic and the philosophy (and foundations) of mathematics, in particular in the philosophy of set theory. 

His work focuses on the set-theoretic multiverse, new axioms (and their justification), mathematical platonism, abstraction principles and neo-logicism, and the history of logic. 

He is the author of several specialised articles and of two monographs on these topics.