Every single math question about real numbers has a definite true or false answer, even if the world's most famous logic system says it is impossible to know.
A new axiomatic foundation for core mathematics allows us to bypass the undecidability of the standard ZFC system. For decades, mathematicians have accepted that some fundamental questions are simply unanswerable within our current rules. This new approach provides a model that gives a definite value to any assertion about real numbers. We usually think of math as the ultimate realm of absolute truth. This shift suggests that our previous absolute truths were just limited by an incomplete set of starting rules.
A Foundation for the Core Mathematician
arXiv · 2605.03868
The foundations of mathematics have long been considered settled by the Zermelo-Fraenkel-Choice axioms. But set theory abounds in models with different truths and even classical questions such as the measurability of projective sets can vary between models. The core of mathematics resides in the study of structures built from the set R of real numbers. This paper proposes a foundation for core mathematics, with both a system of axioms and a definite model of those axioms, in which essentially al