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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...
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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  • 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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