Pseudo-Exponential Structures and Exponential Algebraic Closedness in the Surreal Numbers
Abstract
This work proposes a pseudo-exponential model within the domain of surreal numbers (No), asystematic methodology for solving equations of the form P(x,e^x) = 0 in No, and a formal proof that theexponential-algebraic closedness (EC) axiom is structurally stronger and more comprehensive in the surrealsthan in the real and complex domains. Furthermore, an ECNo axiomatic scheme is proposed, tailored to Hahngeometry, incorporating axioms of surreal rotundity, support freeness, and the transfinite existence of solutions.
Fields of Study & Subjects
Mathematical and Theoretical Analysis
Advanced Topology and Set Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint