Title: On the Boundaries of Constructive Definability in Arithmetic
Subtitle: The Fundamental Limit of the Natural Number Sequence
Description: Abstract:

This paper introduces the concept of a natural number ("Numerus Apoptosis" or "Apoptonumerus"), the attainment of which leads to a fundamental collapse of arithmetic properties. It is proven that any attempt to define a natural number exceeding this value results in a logical contradiction within the framework of standard set theory axioms. The proposed object establishes an absolute set-theoretical limit for the concept of a "natural number."
Subjects: Set theory, large cardinals, limits of computability, Logic & foundations of mathematics