by Jean Barbet | Dec 10, 2024 | Logic, Number Theory, Set Theory
We explore the foundation of natural arithmetic starting from Peano’s axioms within set theory, revealing an innovative approach to conceptualizing natural numbers. We question the traditional use of ordinals and propose an alternative formulation of the axiom... 
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...