by Jean Barbet | Jun 8, 2024 | Logic, Set Theory

Based on the notions of object and class derived from natural logic, we have redefined the concept of set in an intuitive way, thus establishing a natural set theory without resorting to formal logic. This approach is based on six axioms that form the basis of this...
by Jean Barbet | May 24, 2024 | Logic, Set Theory

The revolution in mathematics is that of set theory, which responds both to the problem of a universal and rigorous conceptual language and to that of a single foundation for all mathematical disciplines. Although set theory was Cantor’s original work, the...
by Jean Barbet | Jul 9, 2023 | Logic, Number Theory, Set Theory

Natural arithmetic is the science of natural numbers: it is based on addition, multiplication, natural order and divisibility. Now, all these operations and relations are defined on the basis of the single successor function, whose properties are brought together in...