In this paper we study a new approach to classify mathematical theorems according to their
computational content. Basically, we are asking the question which theorems can be …

We present a list of open questions in reverse mathematics, including some relevant
background information for each question. We also mention some of the areas of reverse …

We study the logical and computational properties of basic theorems of uncountable
mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903 …

The relevance of this question is twofold: 1) Foundational relevance: suppose a formal
system TPA allows one to formalize a great amount of mathematics but can be shown (by …

Reverse mathematics is the study of the relationships between logical axioms and
mathematical theorems. Traditional reverse mathematics studies subsystems of second …

We study the logical and computational properties of basic theorems of uncountable
mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a …

The bulk of ordinary mathematics is naturally developed within higher order (finite type)
arithmetic, which formally treats a structure consisting of natural numbers N and function (al) …

Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics where
the aim is to identify the minimal axioms needed to prove a given theorem from ordinary, ie …

Turing's famous 'machine'model constitutes the first intuitively convincing framework for
computing with real numbers. Kleene's computation schemes S1–S9 extend Turing's …

We investigate the computational properties of basic mathematical notions pertaining to-
functions and subsets of, like finiteness, countability,(absolute) continuity, bounded variation …