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Description

The set theory is the branch of mathematical logic dealing with providing a solid foundation for mathematics, by its axiomatisation, therefore allowing the definition of every mathematical object. The commonly used theory of reference is Zermelo-Fraenkel, but in mathematics it may be useful (or, sometimes, necessary), to take into account different axiom systems, in two directions: the theory can be reduced, by using weaker axioms, or enlarged, by proposing stronger axioms.

The research group deals with classifying mathematical concepts and theorems by different approaches: provability in subsystems of second-order arithmetic (reverse mathematics), classifying computational content (computable analysis), reducibility in descriptive set theory. Besides analysing the already existing mathematical concepts, new hypotheses are studied, which enlarge the field of mathematics, thus allowing the study of theorems that are currently independent (that is, neither demonstrable nor contradictory), coming from all fields of mathematics.

The privileged field of action for this research is descriptive set theory, that is the study of classes of subsets of real numbers, or, in the generalised version, of wider Polish spaces, easily definable and therefore having regularity properties.

The group collaborates with several research groups, acknowledged at the international level, in other Italian centres and in several other countries.