👉 Generalized Transfinite Arithmetic Geometry (GTAM) is a theoretical framework that aims to extend classical algebraic geometry and number theory to encompass all possible orders, or "types," of infinities, providing a unified language to describe arithmetic properties across different mathematical structures. It uses large cardinal axioms and transfinite induction to study the arithmetic of schemes, which are geometric objects defined by polynomial equations, over various "types" of ordinals. GTAM seeks to understand how geometric and arithmetic properties behave under these varying ordinal settings, allowing mathematicians to analyze phenomena that are invariant across different levels of infinity. This approach has significant implications for number theory, algebraic geometry, and logic, offering new insights into the nature of mathematical truth and the foundations of arithmetic.
