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The Axiom of Infinity: Founding Arithmetic in Set Theory

The Axiom of Infinity: Founding Arithmetic in Set Theory

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...
Natural Set Theory: An Ultimate Foundation for Mathematics

Natural Set Theory: An Ultimate Foundation for Mathematics

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...
The axiomatic construction of natural arithmetic

The axiomatic construction of natural arithmetic

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...

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Recent publications

  • The Axiom of Infinity: Founding Arithmetic in Set Theory
  • The higher axioms of natural set theory
  • Natural Set Theory: An Ultimate Foundation for Mathematics
  • Counting in the Infinite with Ordinal Numbers
  • The axiomatic construction of natural arithmetic

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